Conceptual question for Thermodynamics Part 4

PART 4

1. The amount of energy radiated by a body depends on
a.The nature of the surface
b. The area of the surface
c. Temperature of the surface
d. all the above

2. The wavelenght of the radiation emitted by the body depends on
a.The nature of the surface
b. The area of the surface
c. Temperature of the surface
d. all the above

3.A solid sphere and a hollow sphere of same material and size are heated to the same temperature and allowed to cool in the same surounding.If the temperature diffrence between the sphere and surrounding is T.then
a. Both sphere will cool at the same rate for all values of T
b Hollow sphere will cool faster for all values of T
c. Solid sphere will cool faster for all values of T
d. Both sphere will cool at the same rate for small values of T

4. An ideal black body is thrown in the furnace.It is observed that
a. Intially it is the darkest body and at later times the brightest
b. it is the darkest body all the times
c. It cannot be distinguish at all the times
d. Intially it is the darkest body and at later times It cannot be distinguish


5.In which of the following process,convection does not takes place
a. sea and land breeze
b.boiling of the water
c.heating air around the furnace
d.warming of glass of bulb due to filament

6.One end of a metal rod is kept in a furnace.In steady state,the temperature of the rod
a. Increase
b decrease
c. remains constant
d is non uniform

7 what is true for black body
a e=a=1
b emit radiation and absorb radiation
c. refract radiation
d none of the above

8.which one is true about thermal radiation
a. all bodies emit radiation at all temperature
b. Good reflectors are good emitters of thermal radiation
c. Thermal radiation travel in free space with the velocit of light
d. Thermal radiation are not reflected from the mirror

Conceptual question for Thermodynamics

PART 3

1.In a given process of an ideal gas,dW=0 and dQ<0 ,then for a gas
a.dT <0
b. dV>0
c.dP=0
d. dT>0

2.what is true for a free expansion process
a. dW=0
b. dQ=0
c. dU=0
d. all the above

3. Consider the following two statement
A.If heat is added to the system,it temperature must increase
B.If dW >0 then dV >0
a A & B both are correct
b A is correct only
c. B is correct only
d A &B both are wrong

4.what is true of Isothermal process
a. dT>0
b. dT=0
c. dQ=dW
d. none of the above

5. if dU=-dW for a process,the process is
a. Adiabatic
b. Isothermal
c. Isobaric
d. None of the abobe

6.What is true of a cyclic process
a.ΔQ=ΔW
b ΔU=0
c.ΔU >0
d None of the above

7. An ideal gas is taken from state A(P,V) to state B(P/2,2V) along a straight line path in P-V diagram.Select the correct statement from the following
a.The workdone by the gas in process A to B exceeds the work that would be done by it if the system were taken from A to B along a isotherm
b.in the T-V diagram ,the path AB becomes a part of a parabola,
c. In the P-T diagram,the path becomes a part of a parabola
d.In going from A to B,the temperature T of the gas first increase to a maximum and then decrease

8.Let W₁,W₂ are the workdone in the two process A & B by an ideal gas.ΔT_A=ΔT_B. Let C_A and C_B are the molar heat capacities in two process
Also W₁ > W₂. whic of the following is correct
a.C_A=C_B
b.C_A < C_B
c. C_A > C_B
d None of the above.

9.which of the following is correct
a. Molar heat capacity is 0 for PV^y=Constant
b. Molar heat capacity is infinity in adiabatic process
c. Internal energy does not change in Isothermal Process
d. All the above

10.An ideal gas is taken from state A(P₁,V₁) to state B(P₂,V₂) by two method X & Y..which of the following is correct
a.ΔQ₁-ΔW₁=ΔQ₂-ΔW₂
b.ΔU₁=ΔU₂
c. ΔQ₁+ΔW₁=ΔQ₂+ΔW₂
d. None of the above

Conceptual Question of Thermodynamics

PART 2


1.which one is not the assumption in kinetic theory of gases
a.the molecules of the gas are in continual random motion
b. The molecules interact during the collison
c. The molecules are tiny hard sphere undergoing inelastic collision
d. The collison are of short duration

2. There are two statement
A. Equal volumes of all gases at the same temperature T and pressure P contain an equal no of Molecules
B.the no of molecules in one mole of any gas is 6.0255 * 10²².
which one of the following is correct
a. A and B both
b. A only
c B only
d. A and B both are incorrect

3.There are two statement about Ideal gases
A. The V_rms of gas molecules depends on the mass of the gas molecule and the temperature
B. The V_rms is same for all the gases at the same temperature
which one of the following is correct
a. A and B both
b. A only
c B only
d. A and B both are incorrect

4.Choose the correct statement of the following
a. The pressure of the gas is equal to the total kinetic energy of the molecules in a unit volume of the gas
b. The product of pressure and volume of the gas is always constant
c. The average kinetic energy of molecule of the gas is proportional to its absolute temperature
d. The average kinetic energy of molecule of the gas is proportional to the square root of its absolute temperature

5..which one is true according Vander Waal gas equation
a. The attractive forces between the molecules is not negligible
b Volume of the molecules is negligible as compared to the volume occupied by the gas
c. Volume of the molecules is not negligible as compared to the volume occupied by the gas
d. The attractive forces between the molecules is negligible

Solution

Solution of PART 1
1. (a)
There was no restriction for it expansion.So no tensile or compressive force developed.Longitudinal strains happens only when tensile or compressive force developed in the rod.So answer a

2.(c)
3.(d)
4.(c)
5. (a),(b)
6.(b)
7.(a),(c)
Due to thermal expansion,the diameter of the disc as well of the hole will increase.therefore the moment of inertia will increase resulting in a increase in the angular speed.

Solution of PART 2
1 (c)
2. (b)
3. (b)
4.(c)
5. (a),(c)

Solution of PART 3
1. (a)
dU=dQ-dW or dU=dQ as dQ is negative & dW=o
so dU is negative .dU <0 now dU =nC_vdT
so nC_vdT <0 or dT<0
2.(d)
3.(c) as dW=pdV so if dW> 0 the dV >0
4. (b),(c) as temperature is constant.
5. (a)
6. (a),(b)
7. (a),(b),(d)
8. (c)
9.(a),(c)
10. (a),(b)


Solution of PART 4
1. (d)
2. (c)
3. (b)
4. (a)
5. (d)
6. (d)
7. (a),(b)
8.(d)

Conceptual questions of Thermodynamics

PART 1

1. A rod of length L having coefficent of Linear expansion α is lying freely on the floor.it is heated so that temperature changes by ΔT .Find the longitidunal strain developed in the rod
a. 0
b. αΔT
c. -αΔT
d. none of the above

2.if a is coefficent of Linear expansion,b coefficent of areal expansion,c coefficent of Volume expansion.Which of the following is true
a. b=2a
b. c=3a
c. b=3a
d. a=2b

3.which is of them is not used as the measurable properties in thermometer?
a.Resistance of platinum ire
b.Constant volume of gas
c.Contant pressure of gas
d.None of the above

4.when a solid metalic sphere is heated.the largest percentage increase occurs in its
a.Diameter
b. Surface area
c. Volume
d. density

5.the density of the liquid depends upon
a. Nature of the liquid
b. Temperature of the liquid
c. Volume of the liquid
d. Mass of the liquid

6. A metallic sphere has a cavity of diameter D at its center.If the sphere is heated,the diameter of the . cavity will
a. Decrease
b. Increase
c. Remain unchanged
d. none of the above

7.A metallic circular disc having a circular hole at its center rotates about it axis passing through the center and perpendicular to it plane.when the disc is heated
a. Its speed will decrease
b. Diameter will increase
c. Moment of inertia will increase
d. its speed will increase

Quick Recap of Thermodynamics

Notes for Examination


Temperature

Relation between Celsius and fahrenhite scale is

T_F=9/5 T_C + 32°

T_F - Fahrenhite Temperature
T_C - Celsius Temperature

Relation between Celsius and kelvin scale is
T_C = T_K - 273.15 K


T_K - Temperature in Kelvin
T_C - Temperature in celsius


- If R₀ & R₁₀₀ are resistance of metak wire at ice and steam point resp then temp t can be defined corresponding to resistance R_T as follows

T =	(RT-R0)*100
	R100-R0

- The pressure,volume and temperature in kelvin of such gases obey the equation
PV=nRT ----(1)



Thermal expansion
ΔL=αLΔT


Specific Heat Capacity

c =	`Q
	nΔT

Gas Laws
Boyles Law: PV=constant
Charles Law : V/T=constant
Dalton Law of Partial Pressure: P=P₁ + P₂ +P₃
Root mean Square VelocityV_rms=√3RT/M
Mean Square Velocity
V_m=√8RT/&#960M
Average Velocity
V=√2RT/M
Also
V_rms > V_m > V

Average kinetic Energy of Gas=3/2nRT


First law of Thermodynamics

ΔU=Q-W


Gas Processes

Isothermal Process : PV=constant ,ΔU=0,Q=W,Molar Specific Heat=infinity
Adaibatic Process : PV^y=constant,Q=0,ΔU=-W,Molar Specific Heat=zero
Polytropic Process : PVⁿ=constant,Molar Specific Heat=R/y-1 + R/1-n
Volume Constant : P/T=constant W=0,ΔU=Q,Molar Specific Heat=C_v
Pressure Constant : V/T=constant ΔU=Q-W ,Molar Specific Heat=C_P

Internal energy depends on Temperature.
So for same temperature change ΔT
nC_vΔT=Q₁-W₁=Q₂-W₂=Q₃-W₃

Molar Specfic Heat Capacity of any process is given by

C=C_v + Pdv/ndT where n is no of moles of the gas

Workdone by Gas= ∫PdV



Heat Conduction

Q=-KAdT/dx

Wein displacement lawλT⁴=Constant

Stefan's Law
Q=eσT⁴

Newton law of Cooling

dT/dx=b(T-T_s)

Thermal Expansion

- Increase in dimension of body due to increase in temperature is call thermal expansion
- Most of the solid material expand when heated

-Consider a rod of length L then for small change in temperature ΔT,the fractional change in length ΔL/L is directly propertional to ΔT
ΔL/L=αΔT --(2)
or ΔL=αLΔT --(3)
- constant α characterizes the thermal expansion properties of a particulaqr material and it is known as coefficient of linear expansion.
- for materials having no prefential direction,every linear dimension changes according to equation (3) and L could equally well represent the thickness of the rod,side lenght of the square sheet etc
-Normally metals expand more and have high value of α
- Agian consider the intial surface area A of any surface .Now when the temperature of the body is increases by ΔT ,the increase in surface area is given by
ΔA=α_AAΔT ----(4)
where α_A is the coefficient of area expansion
-Similary we can define coefficient of volume expansion as fractional change in volume ΔV/V of a substance for a temperature change ΔT

as ΔV=α_VVΔT ----(5)
- K^-1 is the unit of these coefficents expansions
- These three coefficent are not strictly constant for a substance and these value is depends on temperature range in which they are measured.

Relation between volume and linear coefficient of expansion for solid materail: Consider a solid parallopide with dimension L₁,L₂ and L₃
then volume is
V= L₁L₂L₃
when temperature increase by a amount ΔT then each linear dimension changes and then new volume is
V+ΔV=L₁L₂L₃(1+α_L )
V+ΔV=V(1+α_LΔT)³
V+ΔV=V(1+3α_LΔT+3α_L²ΔT²+α_L³ΔT³)
if ΔT is small the higher order can be neglected.Thus we find
V+ΔV=V(1+3α_LΔT)
ΔV=3α_LVΔT
Comparing this with equation (5) we find
α_V=3α_L

Study Tips for IITJEE

PART 1

1. Concentrate on the basic concepts.Strengthen your fundamentals.Master the basic of each chapter.Do many times so that you know the concept by heart.NCERT books are good for the concept.So first should be to study the NCERT books and familarize all the concepts.HC verma is also good for concept

2. Once you are through with the concepts,you need to develop problem solving skills.Pick one good physics and start solving the questions.Initially problems of low level should be tried and only when you have mastered them,you should go on to solving intricate JEE type problems.ALways give full attempt the question before seeing the solutions.Try to recall all the formula,concepts and try the solve the problems.Dont take too many Physics books .One or two should be sufficent.

3.JEE paper consists of questions from various units.Some units are easiar to solve.So Students should try the following order for mastering the units

Thermodynamics:It is quite simple to master this topics.JEE paper always have few question from it.So easy to score those.
Hydrostatics and Bernoulli's Principle:This is also simple.
Waves in Elastic Media:THis too is simple to master.JEE always have one or two question from it.
Interference Beats and Doppler's Effect:Similarly for this.
Electrostatics :Coloumbs law,Potential,electric question are simple to attempt.
Electromagnetic Induction
Lorentz' Forces:Simple question from it.
Circuits with Capacitors:Easier to attempt with some practice and method to solve the circuits
Modern Physics (full):Always have some question from it.Easiar to master
Collisions:JEE paper have difficult question from this but easiar then below topics.It should attempted in the last
Rotational Motion:bit tough.It should attempted in the last
Gravitation, Elasticity, S.H.M. :bit tough.It should attempted in the last

4 Once you are through with the course.You should start taking Mock test.This will give you the feel of the examination.Try to give as many as possible.Judge your speed and accuracy.You wont feel tensed and stressed on the examination day this way.

5.Make shorts notes for last revision before examination.Those should contains all the important formule which will help you in solving the problems fast.

6. Develop an habbit of judgeing the question .You should be able to judge the question whether you should go for it or not.This is very important thing.There will always few question in JEE paper which will be very tough.If you put your head in those question,you will waste your time and you will not any thing.SO it is important to judge the question.You should never attempt any question which you dont know head and tail of it.

7.Before starting doing the IITJEE paper
Step 1: Take a quick glance of the paper so that you are aware what all type of question and what all topics are given.It should be done in first three minutes
Step 2:Search for questions of topics which is strong to you.Read the questions of the topics and if you have done similar type of question and you are confident about it.Attempt that question.Do this for all the topics u are strong in
You will always find few questions in this catogory
Step 3:Now try to find the questions in your strong topics which looks easy and solvable to you
Step 4: Try to find easy and solvable question to u in the topics you are not very strong

Study Tips for IITJEE

PART 1

1. Concentrate on the basic concepts.Strengthen your fundamentals.Master the basic of each chapter.Do many times so that you know the concept by heart.NCERT books are good for the concept.So first should be to study the NCERT books and familarize all the concepts.HC verma is also good for concept

2. Once you are through with the concepts,you need to develop problem solving skills.Pick one good physics and start solving the questions.Initially problems of low level should be tried and only when you have mastered them,you should go on to solving intricate JEE type problems.ALways give full attempt the question before seeing the solutions.Try to recall all the formula,concepts and try the solve the problems.Dont take too many Physics books .One or two should be sufficent.

3.JEE paper consists of questions from various units.Some units are easiar to solve.So Students should try the following order for mastering the units

Thermodynamics:It is quite simple to master this topics.JEE paper always have few question from it.So easy to score those.
Hydrostatics and Bernoulli's Principle:This is also simple.
Waves in Elastic Media:THis too is simple to master.JEE always have one or two question from it.
Interference Beats and Doppler's Effect:Similarly for this.
Electrostatics :Coloumbs law,Potential,electric question are simple to attempt.
Electromagnetic Induction
Lorentz' Forces:Simple question from it.
Circuits with Capacitors:Easier to attempt with some practice and method to solve the circuits
Modern Physics (full):Always have some question from it.Easiar to master
Collisions:JEE paper have difficult question from this but easiar then below topics.It should attempted in the last
Rotational Motion:bit tough.It should attempted in the last
Gravitation, Elasticity, S.H.M. :bit tough.It should attempted in the last

4 Once you are through with the course.You should start taking Mock test.This will give you the feel of the examination.Try to give as many as possible.Judge your speed and accuracy.You wont feel tensed and stressed on the examination day this way.

5.Make shorts notes for last revision before examination.Those should contains all the important formule which will help you in solving the problems fast.

6. Develop an habbit of judgeing the question .You should be able to judge the question whether you should go for it or not.This is very important thing.There will always few question in JEE paper which will be very tough.If you put your head in those question,you will waste your time and you will not any thing.SO it is important to judge the question.You should never attempt any question which you dont know head and tail of it.

7.Before starting doing the IITJEE paper
Step 1: Take a quick glance of the paper so that you are aware what all type of question and what all topics are given.It should be done in first three minutes
Step 2:Search for questions of topics which is strong to you.Read the questions of the topics and if you have done similar type of question and you are confident about it.Attempt that question.Do this for all the topics u are strong in
You will always find few questions in this catogory
Step 3:Now try to find the questions in your strong topics which looks easy and solvable to you
Step 4: Try to find easy and solvable question to u in the topics you are not very strong

Physics Syllabus for AIEEE

Units And Measurement
Units for measurement, system of units – S.I., fundamental and derived units. Dimensions and their applications.

Description Of Motion In One Dimenstion
Motion in a straight line, uniform and non-uniform motion, their graphical representation. Uniformly accelerated motion, and its applications

Description Of Motion In Two And Three Dimensions
Scalars and vectors, vector addition, a real number, zero vector and its properties. Resolution of vectors. Scalar and vector products, uniform circular motion and its applications projectile motion.

Laws Of Motion
Force and inertia – Newton ’s Laws of Motion. Conservation of linear momentum and its applications, rocket propulsion, friction – laws of friction

Work, Energy And Power
Concept of work, energy and power. Energy – kinetic and potential. Conservation of energy and its applications, Elastic collisions in one and two dimensions. Different forms of energy.

Rotational Motion And Moment Of Inertia
Centre of mass of a two-particle system. Centre of mass of a rigid body, general motion of a rigid body, nature of rotational motion, torque, angular momentum, its conservation and applications. Moment of Inertia, parallel and perpendicular axes theorem, expression of moment of inertia for ring, disc and sphere.

Gravitation
Acceleration due to gravity, one and two-dimensional motion under gravity. Universal law of gravitation, variation in the acceleration due to gravity of the earth. Planetary motion, Kepler’s laws, artificial satellite – geostationary satellite, gravitational potential energy near the surface of earth, gravitational potential and escape velocity.

Solids And Fluids
Inter-atomic and Inter-molecular forces, states of matter.
Solids : Elastic properties, Hook’s law, Young’s modulus, bulk modulus, modulus of rigidity.
Liquids : Cohesion and adhesion. Surface energy and surface tension. Flow of fluids, Bernoulli’s theorem and its applications. Viscosity, Stoke’s Law, terminal velocity.

Oscillations
Periodic motion, simple harmonic motion and its equation of motion, energy in S.H.M., Oscillations of a spring and simple pendulum.

Waves
Wave motion, speed of a wave, longitudinal and transverse waves, superposition of waves, progressive and standing waves, free and forced Oscillations, resonance, vibration of strings and air-columns, beats, Doppler effect.

Heat And Thermodynamics
Thermal expansion of solids, liquids and gases and their specific heats, Relationship between Cp and Cv for gases, first law of thermodynamics, thermodynamic processes. Second law of thermodynamics, Carnot cycle, efficiency of heat engines. Transference Of Heat,Modes of transference of heat. Thermal conductivity. Black body radiations, Kirchoff’s Law, Wien’s law, Stefan’s law of radiation and Newton ’s law of cooling.

Electrostatics
Electric charge – its unit and conservation, Coulomb’s law, dielectric constant, electric field, lines of force, field due to dipole and its behaviour in a uniform electric field, electric flux, Gauss’s theorem and its applications. Electric potential, potential due to a point charge. Conductors and insulators, distribution of charge on conductors. Capacitance, parallel plate capacitor, combination of capacitors, energy of capacitor.

Current Electricity
Electric current and its unit, sources of energy, cells- primary and secondary, grouping of cells resistance of different materials, temperature dependence, specific resistivity, Ohm’s law, Kirchoff’s law, series and parallel circuits. Wheatstone Bridge with their applications and potentiometer with their applications.

Thermal And Chemical Effects Of Currents
Heating effects of current, electric power, simple concept of thermo-electricity – Seeback effect and thermocouple, Chemical effect of current – Faraday’s laws of electrolysis.

Magnetic Effects Of Currents
Oersted’s experiment, Bio-Savert’s law, magnetic field due to straight wire, circular loop and solenoid, force on a moving charge in a uniform magnetic field (Lorentz force), forces and torques on currents in a magnetic field, force between two current carrying wires, moving coil galvanometer and conversion to ammeter and voltmeter.

Magnetostatics
Bar magnet, magnetic field, lines of force, torque on a bar magnet in a magnetic field, earth’s magnetic field, para, dia and ferro magnetism, magnetic induction, magnetic susceptibility.

Electromagnetic Induction And Alternating Currents
Induced e.m.f., Faraday’s Law, Lenz’s Law, Self and Mutual Inductance, alternating currents, impedance and reactance, power In a.c. Circuits with L.C. And R Series Combination, resonant circuits. Transformer and A.C. generator.

Ray Optics
Reflection and refraction of light at plane and curved surfaces, total internal reflection, optical fibre; deviation and dispersion of light by a prism; Lens formula, magnification and resolving power; microscope and telescope.

Wave Optics
Wave nature of light; Interference – Young’s double slit experiment. Diffraction - diffraction due to a single slit. Elementary idea of polarization.

Electromagnetic Waves
Electromagnetic waves and their characteristics, Electromagnetic wave spectrum from gamma to radio waves – propagation of EM waves in atmosphere.

Electron And Photons
Charge on an electron, e/m for an electron, photoelectric effect and Einstein’s equation of photoelectric effect.

Atoms, Molecules And Nuclei
Alpha - particles scattering experiment, Atomic masses, size of the nucleus; radioactivity; Alpha, beta and gamma particles/ rays and their properties, radioactive decay law, half life and mean life of radio-active nuclei, binding energy, mass energy relationship, nuclear fission and nuclear fusion.

Solids And Semi-Conductors Devices
Energy bands in solids, conductors, insulators and semi-conductors, pn junction, diodes, diode as rectifier, transistor action, transistor as an amplifier.

Physics Syllabus for IITJEE

General:

Units and dimensions
Dimensional analysis
least count
significant figures
Methods of measurement and error analysis for physical quantities pertaining to the following experiments: Experiments based on using Vernier calipers and screw gauge (micrometer), Determination of g using simple pendulum, Young’s modulus by Searle’s
method, Specific heat of a liquid using calorimeter, focal length of a concave mirror and a convex lens using u-v method, Speed of sound using resonance column, Verification of Ohm’s law using voltmeter and ammeter, and specific resistance of the material of a wire using meter bridge and post office box.

Mechanics I:

Kinematics in one and two dimensions (Cartesian coordinates only), projectiles
Uniform Circular motion
Relative velocity.
Newton’s laws of motion
Inertial and uniformly accelerated frames of reference
Static and dynamic friction
Kinetic and potential energy
Work and power
Conservation of linear momentum and mechanical energy.
Systems of particles
Centre of mass and its motion
Impulse
Elastic and inelastic collisions.
Law of gravitation
Gravitational potential and field
Acceleration due to gravity
Motion of planets and satellites in circular orbits
Escape velocity.

Mechanics II:

Rigid body
moment of inertia
parallel and perpendicular axes theorems
moment of inertia of uniform bodies with simple geometrical shapes
Angular momentum
Torque
Conservation of angular momentum
Dynamics of rigid bodies with fixed axis of rotation
Rolling without slipping of rings
cylinders and spheres
Equilibrium of rigid bodies
Collision of point masses with rigid bodies.
Hooke’s law
Young’s modulus.

FLUID MECHANICS:

Pressure in a fluid
Pascal’s law
Buoyancy
Surface energy and surface tension
capillary rise
Viscosity (Poiseuille’s equation excluded)
Stoke’s law
Terminal velocity
Streamline flow
equation of continuity
Bernoulli’s theorem and its applications.

WAVES AND OSCILLATION:

Linear and angular simple harmonic motions.
Wave motion (plane waves only)
longitudinal and transverse waves
superposition of waves
Progressive and stationary waves
Vibration of strings and air columns
Resonance; Beats
Speed of sound in gases
Doppler effect (in sound).

Thermodynamics:

Thermal expansion of solids, liquids and gases
Calorimetry
latent heat
Heat conduction in one dimension
Elementary concepts of convection and radiation
Newton’s law of cooling
Ideal gas laws
Specific heats (Cv and Cp for monoatomic and diatomic gases)
Isothermal and adiabatic processes
bulk modulus of gases
Equivalence of heat and work
First law of thermodynamics and its applications (only for ideal gases)
Blackbody radiation
absorptive and emissive powers
Kirchhoff’s law
Wien’s displacement law
Stefan’s law.

Electricity And Magnetism:

Coulomb’s law
Electric field and potential
Electrical potential energy of a system of point charges and of electrical dipoles in a uniform electrostatic field
Electric field lines
Flux of electric field
Gauss’s law and its application in simple cases, such as, to find field due to infinitely long straight wire
uniformly charged infinite plane sheet and uniformly charged thin spherical shell.
Capacitance
Parallel plate capacitor with and without dielectrics
Capacitors in series and parallel
Energy stored in a capacitor.
Electric current
Ohm’s law; Series and parallel arrangements of resistances and cells; Kirchhoff’s laws and simple applications; Heating effect of current.
Biot–Savart’s law and Ampere’s law
Magnetic field near a current-carrying straight wire, along the axis of a circular coil and inside a long straight solenoid;
Force on a moving charge and on a current-carrying wire in a uniform magnetic field.
Magnetic moment of a current loop
Effect of a uniform magnetic field on a current loop
Moving coil galvanometer, voltmeter, ammeter and their conversions.
Electromagnetic induction
Faraday’s law, Lenz’s law
Self and mutual inductance
RC, LR and LC circuits with d.c. and a.c. sources.

Optics:

Rectilinear propagation of light
Reflection and refraction at plane and spherical surfaces
Total internal reflection
Deviation and dispersion of light by a prism
Thin lenses
Combinations of mirrors and thin lenses
Magnification.
Wave nature of light
Huygen’s principle, interference limited to Young’s double-slit experiment.

Modern physics:

Atomic nucleus
Alpha, beta and gamma radiations
Law of radioactive decay
Decay constant
Half-life and mean life
Binding energy and its calculation
Fission and fusion processes
Energy calculation in these processes.
Photoelectric effect
Bohr’s theory of hydrogen-like atoms
Characteristic and continuous X-rays
Moseley’s law
de Broglie wavelength of matter waves.

IITJEE Test series Electric Potential

Multiple choice question with only one answer

1.The elctrical potential energy of an islolated metal sphere of radius R and total Charge Q
a. Q²/4πεR
b. Q²/8πεR
c. Q²/2πεR
d. Q²/16πεR


2. A electric dipole is placed at +q(-a,0) and -q(a,o) in the xy plane.Find the workdone by the electric lines on charge which is moved from point (0,a) to (0,-a).
a. zero
b. p/4πεr²
c. -p/4πεr²
d. none of the above


3.Find the electric field at the centre of the uniformly charged semicircular arc of of Radius R and linear charge density λ
a.λ/2πεa
b.λ/4πεa
c. λ/πεa
d. none of these


4.An electric dipole placed in a uniform electric field experiences
a. A torque but no force
b A force but no torque
c. Both force and torque
d neither a force and torque

5.A charge q is placed at the center of the line joining two equal charges Q.The system of three charges will be in equilibrium if q equal is
a. -Q/2
b. Q/2
c. Q/4
d. -Q/4



Multiple choice questions with one or more answer

6.Choose the correct statement
a.if electric field is zero at the point then electric potential must be also zero at that point
b.Two diffrent equipotential surface can intersect
c.if electric potential is constant in a given region then electric field must be zero in that region
d. Electrons move from higher potential to lower potential



7.A spherical conductor shell has charge Q on it and Radius of the spherical shell is R
a. Electric potential decrease with 0< r < infinity
b Electric field decrease with with 0< r < infinity
c Electric potential is non zero constant for 0< r < =R and decrease for R< r < infinity
d Electric field is zero for 0< r < =R and decrease for R< r < infinity

8.Electric potential V(x,y) of a electrostatic field E=a(yi +xj) where a is constant
a.V(x,y)-V(0,0)=-axy
b.V(x,y)-V(1,1)=-axy+a
c.V(x,y)-V(1,1)=-axy-a
d. None of the these


Assertion and Reason
a) Statement I is true ,statement II is true ,statement II is correct explanation for statement I
b) Statement I is true ,statement II is true ,statement II is not a correct explanation for statement I
c) Statement I is true,Statement II is false
d) Statement I is False,Statement II is True

9.
STATEMENT I:Electrix flux through any closed surface around point charge is independent of the size and shape
STATEMENT II.φ=∫ E.da



10.
STATEMENT I:Electric potential inside the spherical conductor shell is nonzero constant
STATEMENT II:Electric field inside the shell is zero



11.
STATEMENT I:Electric Field on the surface of a conductor is less at the sharp corners

STATEMENT II: Surface charge density on conductor surface is inversely proportional to the radius of curvature

IIT JEE Test Series(Electricity-1)

IIT JEE Test Series(Electricity-1)

Multiple choice question with only one answer

1.A rod lies along the x-axis with one end at the origin and other at x->∞it caries a uniform charge λ C/m.Find the electric field at the point x=-a on the x-axis
a. -(λ/4πε₀a)i
b.-(λ/4πε₀a²)i
c. (λ/4πε₀a)i
d. (λ/4πε₀a²)i


2.Twelve charges of charge q are situated at the corners of the 12 sided polygon of side a.What is the net force on the charge Q at the center
a. Zero
b. 3qQ/πε₀a²
c. qQ/πε₀a²
d None of the above



3.Two positive point charge are placed at the distance a apart have sum Q.What values of the charges,coulumb force between them is maximum
a.q₁=q₁=Q/2
b. q₁=3Q/4 ,q₂=Q/4
c. q₁=5Q/6 ,q₂=Q/6
d Non of the above


4.A metallic shell having inner radius R₁ and outer radii R₂ has a point charge Q kept inside the cavity.Electric field in the region R₁ < r < R₂ where r is the distance from the center is given by
a depends on the value of r
b zero
c, Constant and nonzero everywhere
d. None of the above


5.Consider two statements
A)The force with which two charges interact is not changed by the presence of the other charges
B)Electric force expierenced by the charge particle due to number of fixed point charges is vector resultant of the forces expierence due to individual charges
a) A and B both are correct
b) A is correct only
c) B is correct only
d. A and B both are wrong

Multiple choice question with more than one answer

6)A metallic sold sphere of radius R is given the charge Q.Which of the following statement is true then
a) Electric field at points 0< r < R is zero
b) Charge Q is on the outer surface of the sphere
c) Electric field at r>R is given by Q/4πε₀r²
d) Electric field is perpendicular to the surface of the sphere



7)A simple pendulum consists of a small sphere of mass and posutive charge q is suspended by the string of length L.The pendulum is placed in the electric field of strength E directed vertically downwards.Which of the following is true
a)Time period of oscillation=T=2π√L/(g+qE/m)
b)Time period of oscillation=T=2π√L/(g-qE/m)
c) Tension in the string when the pendulum is at rest =mq+qE
d)Tension in the string when the pendulum is at rest =mq-qE


8)A rod lies on the x-axis with end end at x=-L and other end at x=L with uniform charge λ C/m.Which of the following is true
a.Electric field at any point (0,y) on the y-axis is given by
E=(2kλL/y√(y²+L²))j
b. For point on the Y-axis greater than y>>>>L
E=(2kλL/y²)j
c. Electric field if L->∞
E=2kλ/y
d. None of the above


9. A particle of mass m and charge q is thrown horizontally with a velocity v from top of the building of height H.An electric field exists in the plane and it is horizontally away from the building
which of the following is true
a) Range of the particle is greater than v√(2H/g)
b) Time of flight is √(2H/g)
c) Path is parabolic
d None of the above



Assertion and Reason
a) Statement I is true ,statement II is true ,statement II is correct explanation for statement I
b) Statement I is true ,statement II is true ,statement II is not a correct explanation for statement I
c) Statement I is true,Statement II is false
d) Statement I is False,Statement II is True

10.
STATEMENT I:There is no electric field in conducter in electrostatics
STATEMENT II:There are plenty of free electron in the conductor which moves in such a way to cancel all the electric field



11.
STATEMENT I:Coulumb law of forces are a action reaction pair
STATEMENT II:Coulumb law of forces are non conservative in nature



12.
STATEMENT I:Two electric lines of forces never intersect
STATEMENT II:Electric lines of forces originate from -ve charge and terminate on +ve charge



13.
STATEMENT I:Excess charge given to conductor always reside on the outer surface
STATEMENT II:E is zero inside the bulk material of the conductor


Matrix Match type
14) A metallic shell is having a charge q at the center.Column I gives the location of the charge,Column II defines the charge distribution on the surface due to the charge.You have to match the statement in Column I to column II

Column I
A) q is at the center
B) q is displaced from the center
C) An excess charge Q is given to the metallic shell
D) An Charge Q is placed near the shell

Column II
P)Charge distribution is uniform at the inner surface of the metallic shell
Q)Charge distribution is non uniform at the inner surface of the metallic shell
R)Charge distribution is uniform at the outer surface of the metallic shell
S)Charge distribution is non uniform at the outer surface of the metallic shell


Linked Comprehension Type

A electric charge q of mass m is projected horizontally with a velocity v in the Uniform elctric field which occupies limited space in the region.Electric field E is vertically upwards.And the limited region of the electric field is of length a.Assuming X axis as horizontal and Y-axis as vertical.And let us assumes charge start from origin in the electric field.
Answer following question based on this

15)Horizontal components and Vertical components of the velocity when it passes through the end of the field i.e at x=a
a)v,qEa/mv
b)v,qE/mv
c)qEa/mv,a
d)qE/mv,v


16) Equation of the motion of the particle
a) staright line
b) parabola
c) circle
d) none of the above



17) if the charge get deflected by angle α when it comes out of electric field ,then which one is true
a) tanα=qEa/mv²
b) tanα=qEa/mv
c) sinα=qEa/mv
d) sinα=qEa/mv²

Multiple choice question with only one answer
1.

Ans (a)

2.

Ans (a)

3.

Ans (A)

4.

Ans (b)

5.
Ans (A)

Multiple choice question with more than one answer

6)

Ans (all)

7)

Ans a,c

8)
Ans a,b,c

9.

Ans a,b


10.

Ans (a)

11.


Ans (c)

12.


Ans (c)

13.

Ans (a)

Matrix Match type



Ans
A-P,R
B-Q,R
C-P,R
D- P,S

Linked Comprehension Type



1)
Ans (a)

2)
Ans (b)

3)

Ans (a)

PMT test series for Mechanics

Multiple choice question with one or more answer

1. A body fall from height H.if t₁ is time taken for covering first half height and
t₂ be time taken for second half.Which of these relation is true for t₁ and t₂
a. t₁ > t₂
b. t₁ < t₂
c t₁=t₂
d Depends on the mass of the body

2.A 1 kg ball moving at 12 m/s collides head on with 2 kg ball moving with 24 m/s in opposite direction.What are the velocities after collision if e=2/3?
a. v₁=-28 m/s,v₂=-4 m/s
b. v₁=-4 m/s,v₂=-28 m/s
c. v₁=28 m/s,v₂=4 m/s
d. v₁=4 m/s,v₂=28 m/s


3.A train running at 30m/s is slowed uniformly to a stop in 44 sec.Find the stopping distance?
a. 612 m
b. 662 m
c. 630 m
d. 605 m

4.A nut comes loose from a bolt on the bottom of an elevator as the elavator is moving up the shaft at 3m/s.The nut strikes the bottom of the shaft in 2 sec.How far from the bottom of the shaft was the elevator when nut falls off?
a. 13.6 m
b. 10 m
c. 12.6 m
d. none of these


5.A system consisting of two objects has a total momentum of (18 kgm/sec)i and its center of mass has the velocity of (3 m/s)i.One of the object has the mass 4 kg and velocity (-1.5 m/s)i.The mass and velocity of the other objects are
a. 2 kg, (6 m/s)i
b. 2 kg, (-6 m/s)i
c. 2 kg, (3 m/s)i
d. 2 kg, (-3 m/s)i


6.A moving bullet hits a solid target resting on a frictionless surface and get embeded in it.What is conserved in it?
a. Momentum Alone
b KE alone
c. Both Momentum and KE
d. Neither KE nor momentum


7.A body of mass 5 kg starts from the origin with an intial velocity u=30i+40j m/sec.If the constant force acts on the body F=-(i+5j) N.The time in which y component of the velocity becomes zero is
a. 5 sec
b. 80 sec
c. 20 sec
d. 40 sec


8. A stationary body of mass 3 kg explodes into three equal parts.Two of the pieces fly off at right angles to each other with the velocities 2i m/s and 3j m/s.If the explosion takes place in 10^-3 sec.find out the average force action on the third piece in N
a.(-2i-3j)10³
b. (2i+3j)10³
c (2i-3j)10^-3
d. none of these


9.A bullet of mass m is fired horizontally with a velocity u on a wooden block of Mass M suspended from a support and get embeded into it.The KE of th wooden + block system after the collisson
a.m²u²/2(M+m)
b.mu²/2
c. (m+M)u²/2
d. mMu²/2(M+m)



10.A body of Mass M and having momentum p is moving on rough horizontal surface.If it is stopped in distance s.Find the value of coefficient of friction
a.p²/2M²gs
b. p/2Mgs
c. p²/2Mgs
d. p/2M²gs



Solutions
1.a
2.a
3. b
4.a
5 a
6 a
7 d
8 a
9 a
10 a

Mechanics Test Series -II

Multiple choice question with one or more answer
1. A block of mAss M is moving with a velocity v on straight surface.What is the shortest distance and shortest time in which the block can be stopped if μ is coefficent of friction
a.v²/2μg,v/μg
b. v²/μg,v/μg
c.v²/2Mg,v/μg
d none of the above


2.A horizontal force of F N is necessary to just hold a block stationary against a wall. The coefficient of friction between the block and the wall is μ. The weight of the block is
a.μF
b. F(1+μ)
c. F/μ
d none of these


3.Consider the following two statements.
STATEMENT 1 Linear momentum of a system of particles is zero.
STATEMENT 2 Kinetic energy of system of particles is zero.
(A) A does not imply B and B does not imply A.
(B) A implies B but B does not imply A
(C) A does not imply B but b implies A’
(D) A implies B and B implies A.


4.The Position vector of the center of mass of uniform semi circular ring of radius R and Mass M whose center coincided with the origin
a.r=(2R/π)j
b.r=(R/π)j
c.r=(4R/π)j
d. none of the these

5.A body is sliding down a rough inclined plane of angle of inclination θ for which coefficent of friction varies with distance y as μ(y)=Ky where K is constant.Here y is the distance moved by the body down the plane.The net force on the body is zero at A.Find the value of constant K
a. tanθ/A
b. Acotθ
c. cotθ/A
d. A tanθ

6.Chosse the correct option
a.if Workdone by the conservative force is positive then Potential energy decreases
b. Rate of change of momentum of many particles system is proportional to net external force on the system
c.The workdone by the conservative force in closed loop is zero
d. None of the above

7.Two electrons(e) are the at the point (-a,0) and (a,0).Their mass is m.They are released from rest.The acceleration of the center of mass of the system when the electron at 4a distance apart
a. e²/64mπε₀a²
b. zero
c. e²/16mπε₀a²
d. none of the above

8.The potential energy of a certain particle is given by
U=20x²+35z³.Find the vector force on it
a. -40xi-105z²k
b. 40xi-105z²k
c.-10xi-105z²k
d 40xi+105z²k

Matrix Match type

9.
Column I
a. Frictional force
b. Gravitational force
c. Electrical force
d Viscous force

Column II
P. Workdone by the force in closed loop is zero
Q. Workdone by the force in closed loop is not zero

IITJEE TestSeries Mechanics -1

Multiple choice question with one answer

1.A IITJEE text book of mass M rests flat on a horizontal table of mass m placed on the ground.Let R_X->Y be the constant force exerted by the body x on body Y.According to Newton third law,which of the following is an action-reaction pair of forces?

a. (M+m)g and R_table->book
b. R_{ground->table} and mg+R_book->table
c. R_{ground->table} and R_{table->ground}
d Mg and R_table->book


2. there are two statements
A Newtons first law in valid from the pilot in an aircraft which is taking off
B Newtons first law in valid from the observer in a train moving with constant velocity
Which of the following is correct

(a) A only
(b) B only
(c) Both A and B are correct
(d) Both A and B are wrong


3.The horizontal and vertical displacement of the projectile at time t are
x=36t
y=48t-4.9t²
where x and y are in meters and t in second.Intial velocity of the projectile in m/s
a. 15
c. 30
b. 45
d. 60


4.A truck accelerates from rest at the constant rate a for some time after which it decelerates at a constant rate of b to come to the rest.If the total time elapsed is t ,then find out the maximum velocity attains by the truck
a. (ab/a+b)t
b.(a+b/ab)t
c. (a²+b²/ab)t
d.(a²-b²/ab)t


5.A boy playing on the roof of a 10 m high building throws a ball with a speed of 10 m/s at an angle of 30 ° with the horizontal. How far from the throwing point will the ball be at the height of 10 m from the ground? take g = 10 m/s²
a. 5.20 m
b.4.33 m
c.2.60 m
d 8.66 m.

Multiple choice question with one or more answer

1. A body is projected horizontally from a point above the ground.The motion of body is defined as
x=2t
y=2t²
where x and y are horizontal and vertical displacement respectivley at time t.Which one of the following is true
a.The trajectory of the body is a parabola
b The trajectory of the body is a straight line
c.the velocity vector at point t is 2i+4tj
d the acceleration vector at time t is 4j


2.Mark out the correct statement
a)Instantaneous Velocity vector is always in the direction of the motion
b)Instantaneous acceleration vector is always in the direction of the motion
c)Acceleration of the moving particle can change its direction with any change in direction of velocity
d) None of the above




Assertion and Reason
a) Statement I is true ,statement II is true ,statement II is correct explanation for statement I
b) Statement I is true ,statement II is true ,statement II is not a correct explanation for statement I
c) Statement I is true,Statement II is false
d) Statement I is False,Statement II is True

1. STATEMENT1: The Average velocity of a continously moving particle may be zero for some time interval but average speed will not be zero
STATEMENT: Displacement of a continously moving particle can decrease with time but distance will not


2. STATEMENT1: Two bodies of mass m and M will reach ground in same time when fallen at same time from the tower of height h
STATEMENT1: Same Acceleration due to gravity is experienced by the both body in fall from tower


3.STATEMENT1:In a projectile motion,acceleration vector is Perpendicular to Velocity vector at the highest point
STATEMENT:There is no horizontal acceleration present in the projectile motion




Matrix match type
In a free fall motion from rest,Match column I to column II
column I
A) Graph between displacement and time
B) Graph between velocity and time
C) Graph between velocity and displacement
D) Graph between KE and displacement

column II
P) Parabola
Q) Straight line
C) Circle
D) No appropiate match given

Linked Comphrehension type
.A train is moving in the west direction with a velocity 15m/s.A monkey runs on the roof of the train against its motion with a velocity 5m/s with respect to train .Take the motion along west as positive
1.Velocity of train relative to its driver
a. 0
b. 15 m/s
c. -15 m/s
d. 20 m/s

2. What is the velocty of train with respect to monkey
a. 5m/s
b -5 m/s
c. 15 m/s
d -15 m/s

3. find the velocty of ground with respect to monkey
a. 5 m/s
b. -5 m/s
c. 10 m/s
d. -10 m/s

Conceptual Questions of waves

1. Transverse wave velocity in a stretched string depends on
a. frequency of wave
b. tension
c. length of string
d. linear mass density string


2. A transverse wave travels along the x axis.The particles of the medium must move
a. Along the z-axis
b Along the x-axis
c. In the Y-Z plane
d. Along the y axis



3.What is true for a standing wave on the string
a.All the particles are never at rest simultaneously
b. In one complete cycle,all the particles cross their mean position simultaneously twice
c. In one complete cycle,all the particles cross their mean position simultaneously once
d. All the particles acquire their positive extreme positions simultaneously once in a cycle



4.Choose the incorrect one
a. When a ultrasonic wave travels from air into water.It bends towards the normal to the air-water interface
b.Any function of the form y(x,t)=f(vt+x) represents a travelling wave
c.the velocity ,wavelenght and frequency of wave undergo change when it is reflected from a surface
d. None of the above

5.Match the following with the types of the wave

A) Thermal radiation received from the sun
B)Sound waves produced by the vibrating string of guitar
C) Radio waves sent out from broadcasting station
D)X Rays
E) Waves produced in the air by the vibrating tuning fork

P) longitudinal
Q) Transverse





6. Which of the following functions represent a travelling wave
a. y=pcos(qx)sin(rt)
b. y=psin(qx+rt)
c. y=psin(qx-rt)
d. none of the above


7. Which of the following is not a standing wave
a. y=pcos(qx)sin(rt)
b. y=psin(qx+rt)+psin(qx-rt)
c. y=psin(qx+rt)
d Non of the above



8. When a wave is refracted into another medium which of the following will change
a. Velocity
b. Frequency
c. Phase
d. Amplitude

9.A pipe closed at one end and open at other will give
a. All even harmonics
b, All odd harmonics
c. All the harmonics
d. None of the harmonics



10. To raise the pitch of a stringed musical instrument ,the player can
a. Lossen the string
b. Tighten the string
c. Shorten the string
d. Lengthen the string


1.Ans. b,d

2. Ans c

3.Ans b,d

4.a,c

5.Ans A-Q,B-P,C-Q,D-Q,E-P


6. ans b,c

7. Ans c


9.Ans c


10. Ans b,c

Test Series IIT JEE (Electricity-1)

Multiple choice question with only one answer

1.A rod lies along the x-axis with one end at the origin and other at x->∞it caries a uniform charge λ C/m.Find the electric field at the point x=-a on the x-axis
a. -(λ/4πε₀a)i
b.-(λ/4πε₀a²)i
c. (λ/4πε₀a)i
d. (λ/4πε₀a²)i


2.Twelve charges of charge q are situated at the corners of the 12 sided polygon of side a.What is the net force on the charge Q at the center
a. Zero
b. 3qQ/πε₀a²
c. qQ/πε₀a²
d None of the above



3.Two positive point charge are placed at the distance a apart have sum Q.What values of the charges,coulumb force between them is maximum
a.q₁=q₁=Q/2
b. q₁=3Q/4 ,q₂=Q/4
c. q₁=5Q/6 ,q₂=Q/6
d Non of the above


4.A metallic shell having inner radius R₁ and outer radii R₂ has a point charge Q kept inside the cavity.Electric field in the region R₁ < r < R₂ where r is the distance from the center is given by
a depends on the value of r
b zero
c, Constant and nonzero everywhere
d. None of the above


5.Consider two statements
A)The force with which two charges interact is not changed by the presence of the other charges
B)Electric force expierenced by the charge particle due to number of fixed point charges is vector resultant of the forces expierence due to individual charges
a) A and B both are correct
b) A is correct only
c) B is correct only
d. A and B both are wrong

Multiple choice question with more than one answer

6)A metallic sold sphere of radius R is given the charge Q.Which of the following statement is true then
a) Electric field at points 0< r < R is zero
b) Charge Q is on the outer surface of the sphere
c) Electric field at r>R is given by Q/4πε₀r²
d) Electric field is perpendicular to the surface of the sphere



7)A simple pendulum consists of a small sphere of mass and posutive charge q is suspended by the string of length L.The pendulum is placed in the electric field of strength E directed vertically downwards.Which of the following is true
a)Time period of oscillation=T=2π√L/(g+qE/m)
b)Time period of oscillation=T=2π√L/(g-qE/m)
c) Tension in the string when the pendulum is at rest =mq+qE
d)Tension in the string when the pendulum is at rest =mq-qE


8)A rod lies on the x-axis with end end at x=-L and other end at x=L with uniform charge λ C/m.Which of the following is true
a.Electric field at any point (0,y) on the y-axis is given by
E=(2kλL/y√(y²+L²))j
b. For point on the Y-axis greater than y>>>>L
E=(2kλL/y²)j
c. Electric field if L->∞
E=2kλ/y
d. None of the above


9. A particle of mass m and charge q is thrown horizontally with a velocity v from top of the building of height H.An electric field exists in the plane and it is horizontally away from the building
which of the following is true
a) Range of the particle is greater than v√(2H/g)
b) Time of flight is √(2H/g)
c) Path is parabolic
d None of the above



Assertion and Reason
a) Statement I is true ,statement II is true ,statement II is correct explanation for statement I
b) Statement I is true ,statement II is true ,statement II is not a correct explanation for statement I
c) Statement I is true,Statement II is false
d) Statement I is False,Statement II is True

10.
STATEMENT I:There is no electric field in conducter in electrostatics
STATEMENT II:There are plenty of free electron in the conductor which moves in such a way to cancel all the electric field



11.
STATEMENT I:Coulumb law of forces are a action reaction pair
STATEMENT II:Coulumb law of forces are non conservative in nature



12.
STATEMENT I:Two electric lines of forces never intersect
STATEMENT II:Electric lines of forces originate from -ve charge and terminate on +ve charge



13.
STATEMENT I:Excess charge given to conductor always reside on the outer surface
STATEMENT II:E is zero inside the bulk material of the conductor


Matrix Match type
14) A metallic shell is having a charge q at the center.Column I gives the location of the charge,Column II defines the charge distribution on the surface due to the charge.You have to match the statement in Column I to column II

Column I
A) q is at the center
B) q is displaced from the center
C) An excess charge Q is given to the metallic shell
D) An Charge Q is placed near the shell

Column II
P)Charge distribution is uniform at the inner surface of the metallic shell
Q)Charge distribution is non uniform at the inner surface of the metallic shell
R)Charge distribution is uniform at the outer surface of the metallic shell
S)Charge distribution is non uniform at the outer surface of the metallic shell


Linked Comprehension Type

A electric charge q of mass m is projected horizontally with a velocity v in the Uniform elctric field which occupies limited space in the region.Electric field E is vertically upwards.And the limited region of the electric field is of length a.Assuming X axis as horizontal and Y-axis as vertical.And let us assumes charge start from origin in the electric field.
Answer following question based on this

15)Horizontal components and Vertical components of the velocity when it passes through the end of the field i.e at x=a
a)v,qEa/mv
b)v,qE/mv
c)qEa/mv,a
d)qE/mv,v


16) Equation of the motion of the particle
a) staright line
b) parabola
c) circle
d) none of the above



17) if the charge get deflected by angle α when it comes out of electric field ,then which one is true
a) tanα=qEa/mv²
b) tanα=qEa/mv
c) sinα=qEa/mv
d) sinα=qEa/mv²


Multiple choice question with only one answer
1.

Ans (a)

2.

Ans (a)

3.

Ans (A)

4.

Ans (b)

5.
Ans (A)

Multiple choice question with more than one answer

6)

Ans (all)

7)

Ans a,c

8)
Ans a,b,c

9.

Ans a,b


10.

Ans (a)

11.


Ans (c)

12.


Ans (c)

13.

Ans (a)

Matrix Match type



Ans
A-P,R
B-Q,R
C-P,R
D- P,S

Linked Comprehension Type



1)
Ans (a)

2)
Ans (b)

3)

Ans (a) 

Test Series for IITJEE SHM

Mulitiple choice questions with one answer

1.The amplitutde and phase of a particle executing SHM depends on
a.The displacemnt of particle at t=0
b.The velocity of particle at t=0
c Both Velocity and displacement at t=0
d Neither velocity and displacemnt at t=0


2.A particle of mass m is attached to a massless string of lenght L and is oscillating in vertical plane with one end of string fixed to rigid support.Tension in the string at a certain instant is T=kmg.Then
a. K can never be equal to 1
b. K can never be greater than 1
c. K can never be greater than 3
d K can never be less than 1

3. A particle is executing SHM at mid point of mean position and extreme position . What is it's KE in terms of total energy E.

(a) E/2
(b) 4E/3
(c) √ 2E
(d) 3E/4

4. A spring of force constant k is cut into two pieces such that one piece is four times the length of the other. the longer piece will have force constant equal to

(a) 4k/5
(b) 5k/4
(c) 3k/2
(d) 4k

5. Total energy of mass spring system in harmonic motion is E=1/2(mω²A²). Consider another system executing SHM with same amplitude having value of spring constant as half the previous one and mass twice as that of previous one. The energy of second oscillator will be

(a) E
(b) 2E
(c) √ 2E
(d) E/2

Mulitiple choice questions with more then one answer

6.For a particle executing SHM
a.Acceleration is proportional to the displacement in the direction of the motion
b.Acceleration is proportional to the displacement but in opposite direction of the motion
c. Total energy of particle remains constant
d KE and PE of particle remains constant


7. which one of the following statement is true
a. Maximum value of velocity in SHM is A²ω
b.In SHM velocity of the particle is maximum when displacment is maximum
c.Velocity of the particle is zero in SHM when displacement attains its maximum on either side
d.Velocity in SHM vary periodically with time


8. which one of the following statement is true
a. Amplitude and intial displacement of particle in SHM are always equal
b.Amplitude and intial displacement of particle in SHM are never equal
c. Amplitnude of a particle in SHM can be equal to its initial displacement
d. Amplitnude of a particle in SHM can be greater to its initial displacement


9.To execute SHM system must have
a. Elasticity
b. Moment of Inertia
c. Inertia
d. all the above


10. Angular frequency of system executing SHM depends on
a. mass
b. total energy
c.force constant
d. Amplitude


Assertion and Reason
a) Statement I is true ,statement II is true ,statement II is correct explanation for statement I
b) Statement I is true ,statement II is true ,statement II is not a correct explanation for statement I
c) Statement I is true,Statement II is false
d) Statement I is False,Statement II is True

11.
STATEMENT 1:Frequency of oscillation in Simple pendulum depends on Amplitude of oscillation
STATEMENT 2:Timeperiod of oscillation in simple pendulum is given by T=2π√L/g

12.
STATEMENT 1:Total energy remains constant in SHM
STATEMENT 2:KE is maximum at mean position

13.
STATEMENT 1:The quantity F.r where F is force and r is displacement is negative in SHM
STATEMENT 2:THe quantity a.r where a is acceleration and r is displacement is positive in SHM

14.
STATEMENT 1:The amplitude or energy is defined by the intial position and intial velocity in SHM
STATEMENT 2:THe phase of motion is determined by the intial position and intial velocity in SHM

MAtrix match type

15.
In a spring mass system executing SHM having mass m and spring constant K with Timeperiod T.Match the column I to the column II

Column I
A) Amplitude is doubled
B) Mass is doubled
C) Spring constant is doubled and mass is 2 doubled also
D)Amplitude is doubled and spring constant is made half

Column II
A) Timeperiod is T
B) Timeperiod is T√2
C) Timeperiod is 2T
D) no match is appropiate


Linked Comphrehension Type
A block of mass M₁ resting on the frictionless surface is connected to a spring of spring constant K that is anchored in the nearby wall.A block of mass M₂=aM₁ is placed on the top of the first block.The coefficent of static friction between the two bodies is μ_s

16 Assuming the two bodies moves as single object,find the period of oscillation of the system
a T=2π√(1+a)M₁/k
b T=2π√M₁/k
c. T=2π√(1-a)M₁/k
d. None of the above

17. Find the maximum oscillation magnitude A_max that permits the two bodies to move as unit
a. A_max=(1+a)μ_sgM₁/k
b. A_max=μ_sgM₁/k
c. A_max=μ_sgM₂/k
d. none of the above

18.find the maximum static frictional force on the body M₂
a. μ_sgM₁
b. μ_sgM₂
c. μ_sgaM₁
d. none of the above

Testseries IITJEE Thermodynamics -I

Mulitiple Choice questions with Single answer
1. A rod of length L having coefficent of Linear expansion α is lying freely on the floor.it is heated so that temperature changes by ΔT .Find the longitidunal strain developed in the rod
a. 0
b. αΔT
c. -αΔT
d. none of the above

2.if a is coefficent of Linear expansion,b coefficent of areal expansion,c coefficent of Volume expansion.Which of the following is true
a. b=2a
b. c=3a
c. b=3a
d. a=2b

3. There are two statement
A. Equal volumes of all gases at the same temperature T and pressure P contain an equal no of Molecules
B.the no of molecules in one mole of any gas is 6.0255 * 10²².
which one of the following is correct
a. A and B both
b. A only
c B only
d. A and B both are incorrect

4.There are two statement about Ideal gases
A. The V_rms of gas molecules depends on the mass of the gas molecule and the temperature
B. The V_rms is same for all the gases at the same temperature
which one of the following is correct
a. A and B both
b. A only
c B only
d. A and B both are incorrect

5. Consider the following two statement
A.If heat is added to the system,it temperature must increase
B.If dW >0 then dV >0
a A & B both are correct
b A is correct only
c. B is correct only
d A &B both are wrong

Mulitiple Choice questions with More than one answer
6.which of the following is correct
a. Molar heat capacity is 0 for PV^y=Constant
b. Molar heat capacity is infinity in adiabatic process
c. Internal energy does not change in Isothermal Process
d. All the above

7.An ideal gas is taken from state A(P₁,V₁) to state B(P₂,V₂) by two method X & Y..which of the following is correct
a.ΔQ₁-ΔW₁=ΔQ₂-ΔW₂
b.ΔU₁=ΔU₂
c. ΔQ₁+ΔW₁=ΔQ₂+ΔW₂
d. None of the above

8 what is true for black body
a e=a=1
b emit radiation and absorb radiation
c. refract radiation
d none of the above

Assertion and Reason
a) Statement I is true ,statement II is true ,statement II is correct explanation for statement I
b) Statement I is true ,statement II is true ,statement II is not a correct explanation for statement I
c) Statement I is true,Statement II is false
d) Statement I is False,Statement II is True
9. STATEMENT 1:The molar specfic heat capacity of the ideal gas in adiabatic process is zero
STATEMENT 2: Heat transfer is zero in the adiabatic process

10.STATEMENT 1:The internal energy between two state is independent of the process path
STATEMENT 2: Internal enerby is intrinsic property of the system

11.STATEMENT 1:Gases behave like ideal gas at high temperature
STATEMENT 2:Intermolecular forces are neglibible at high temperature



Matrix Match type
12. A gas has five molecules having velocities v,2v,3v,4v,5v.Match the column I to column II
column I
P. (V_rms)²
Q. (V_mean)²
R (V²)_mean
S. (V²)_mean - (V_rms)²

column II
W. 9v²
X. 11v²
Y. 10v²
Z. 0

13. Match the column I to column II
column I
P Adiabatic expansion
Q Isothermal compression
C Constant Presure expansion
D.Constant Volume with increase in pressure

column II
W. ΔW>0
X. ΔQ>0
Y. ΔW<0
Z. ΔQ<0

Linked Comphrension type
A cylindrical vessel with its axis vertical,contains one mole of a molecular gas at
thermodynamic equilibrium.The upper base of the cylinder can be displaced freely.It is made of glass plate.Atmospheric pressure is P₀ and Temperature of the gas is T₀.mass of the glass plate is m.There is no heat transfer through the wall of the vessel.The gas is heated through radiation through the glass plate for some time such that the upper plate gets displaced by Δh.The radius of the cylinder is r.Find the following

1. Final temperature of the gas when it get displaced by Δh
a.T₀ +Δh(P₀πr²+mg)/R
b.T₀ -Δh(P₀πr²+mg)/R
c. Δh(P₀πr²+mg)/R
d. None of the above

2. Find out the workdone by the gas
a.Δh(P₀πr²+mg)
b.mgΔh
c. Δh(P₀πr²-mg)
d. none of the above


3.Find the total heat gained by the gas
a.Δh(P₀πr²+mg)(C_V/R +1)
b.Δh(P₀πr²-mg)(C_V/R +1)
c.Δhmg(C_V/R +1)
d.none of the above

Current electricity test series

(A) Assertion reason type question.

(a) If both assertion and reason are true and reason is correct explaination of assertion.
(b) If both assertion and reason are true and reason is not correct explaination of assertion.
(c) Assertion is true but reason is false.
(d) both assertion and reason are false.

(1)
Assertion:Wire carrying current is not charged.
Reason:It is because , at any instant number of electrons leaving wire is sometimes equal to the number of electrons flowing in from the battery.


(2)
Assertion:Drift velocity of electrons decreases on increasing temperature of the conductor.
Reason:It is because, on increasing temperature of a conductor , the value of resistivity of it's material increases.


(3)
Assertion:Resistors are connected in series combination in order to increase the resistance of the circuit.
Reason:In series combination potential difference across any resistor is proportional to it's resistance.


(4)
Assertion:A potentiometer measures the potential difference more accurately then a voltmeter.
Reason:Because it has a wire of high resistance and draws a heavy current from external circuit.


(B) Multiple choice questions with only one answer

(5) A constant voltage is applied between the two ends of a uniform metalic wire and some heat is developed in it . The heat developed is doubled if,
(a) both length and radius of wire are halved
(b) both length and radius of wire are doubled
(c) radius of wire is doubled
(d) length of wire is doubled


(6) Kirchoff's first law of electric circuits is based on the law of conservation of
(a) only on mass
(b) only on charge
(c) on charge as well as on energy
(d) on charge as well as on mass


(7)The temperature coefficent of resistance of wire is 0.00125°C^-1. At 300K, it's resistance is 1 ohm. The resistance of wire would be 2 ohm at
(a) 1154K
(b) 1127K
(c) 1167K
(d) 1176K


(8) If the length of the potentiometer wire is increased, then the accuracy in determination of null point
(a) will increase
(b) will decrease
(c) will remain unaffected
(d) can not be decided , untill emf of auxiliary battery is known


(9) Each of the resistance in the network shown in the figure is equal to R. The resistance between terminal A and B is


(a) R
(b) 5R
(c) 3R
(d) 6R




(10)The current voltage graph for a given metallic wire at two different temperatures T₁ and T₂ are shown in the fig. which one of the following option is true


(a) T₁ = T₂
(b) T₁ < T₂
(c) T₁ > T₂
(d) none of the above



Solutions
1.c
2.a
3.b
4.c
5.b
6.b
7.b
8.a
9.a
10.b

Gravitation questions for IITJEE

Gravitation questions for IITJEE

1.Which is of the following statement is true
A) Gravitational constant G value does not depend on the medium between the bodies
B) Gravitational constant G depends on the masses of the bodies and the sizes of the bodies
a A & B both are correct
b only A is correct
c Only B is correcr
d A and B both are wrong

2.If the distance between the earth and sun were half its present value,the number of days in a year would be
a. 64.5
b. 129
c. 182.5
d. 730

3.if both the mass of earth and its radius are decreased by 1%,the value of acceleration of gravity will
a. Decrease by 1%
b Increase by 1%
c. Increase by 2%
d remain unchanged

4. A body weigh W newton of the surface of the earth.Its weight at a height equal to half the radius of the earth will be
a. W/2
b. 2W/3
c. 4W/9
d. W/4

5.when a stone of mass m is falling in th earth of mass M,the acceleration of the earth will be
a zero
b. mg/M
c. Mg/m
d g

6.The weight of the object will be
a. zero at the center of the earth
b.same in all the satellites
c. same at all the points on the surface of the earth
d. none of the above

7.Which is of the following statement is true
A) it is possible to put an artificial satellite in a orbit such a way that it will remain always directly over New Delhi
B) An earth satellite continues to move in the orbit due to centripetal force provided by the burning of the fuel of its engine
a A & B both are correct
b only A is correct
c Only B is correcr
d A and B both are wrong


8. A mass m is divided into two part ym and (1-y)m .For a given seperation,the value of y for which the gravitattional attraction between the two pieces becomes maximum
a. 1/2
b. 3/5
c. 1
d 2

9.Two bodies of mass M and 2M are at rest at infinte seperation.They move towards each other under the mutual gravitaional attraction.Then at seperation r ,which of the following is false
a. The total energy of the system is not zero
b The force between them is zero
c. The center of the mass of the system is movind
d non of the above

10.Choose the correct statement
a. the gravitational forces between the two bodies are an action and reaction pair
b. G and g are constant everywhere
c.The acceleration due to gravity increase due to rotation of the earth
d. none of the above

1.d
2.b
this can derived using kepler law T² =kR³
3.b
4.c
5.b
6.a,c
7.d
8.a
9.c
10.a