Objective questions of wave

1. The amplitude of a wave disturbance propagating in the positive direction is given by y=1/(1+x²) at time t=0 and by y=1/[1+(x-5)²] at t=5 seconds where x and y are in meters.The shape of the wave disturbance does not change during the propagation.The velocity of the wave is
a. 1 m/sec
b. 1.5 m/sec
c. .5 m/sec
d. 2 m/s


2.A transverse wave in a medium is described by the equation

y=Asin²(wt-kx).
The magnitude of the maximum velocity of particles in the medium is equal to that of the wave velocity.if the value of A is
a.λ/2π
b λ/4π
c. λ/π
d 2λ/π


3.A plane progressive wave is represented by the equation
y=cos(2πt-πx)

The equation of the wave with triple of the amplitude and double the frequency
a. y=3cos(4πt-πx)
b. y=3cos(5πt-πx)
c. y=3cos(4πt+πx)
d. y=3cos(3πt-πx)


4. In the above example ,The equation of wave with double of the amplitude and double the frequency but travelling in the opposite direction
a. y=2cos(4πt+πx)
b. y=2cos(5πt-πx)
c. y=2cos(4πt-πx)
d. y=2cos(3πt-πx)

5.The displacement of a particle having wave motion given by
y=cos²(t/4)sin(50t)
This expression may be considered to be a result of the superposition of how many wave motions
a. one
b Two
c. Three
d. Five


6.A wave is represented by the equation
y=(1mm)sin[(60 s^-1)t+(4 m^-1)x]

which one of the following is true
a. Frequency =30/π
b Amplitude=.001mm
c. Maximum Velocity of the Particle 60 mm/sec
d. wave velocity is 100m/s


7.the displacement of the particles in a string streched in the x-direction is represented by y.Among the following expressions for y,those describing wave motion ares
a. cospxsinqt
b p²x²-w²t²
c.cos²(px+wt)
d. cos(p²x²-w²t²)



8.A transverse wave on a string,the string displacement is described as
y(x,t)=1/1+(x-at)²

where a is negative constant
which of the following is true
a. The Shape of the string at t=0 is y=/1+x²
b. The shape of the waveform does not change as its move along the string
c Waveform moves in the -x direction
d. The speed of the waveform is |a|




1.Ans a

2.Ans b

3.Ans a

4. Ans a

5.Ans 3

6.Ans a and c

7.Ans a

8.Ans a,b,c,d 

mechanics test questions

Question 1
A ball is thrown vertically upwards with a velocity u from top of a tower. It strikes the ground with a velocity 3u. The time taken by the ball to reach the ground is given by
(a) u/g
(b) 2u/g
(c) 3u/g
(d) 4u/g

Question 2
A body slides down an inclined plane of inclination . The coefficient of friction down the plane varies in the direct proportion to the distance moved down the plane(=kx). The body will move down the plane with
(a) constant acceleration =gsin
(b) constant acceleration =(gsin-gcos)
(c) constant retardation =(gcos-gsin)
(d) variable acceleration that first decreases from gsin to zero and that becomes negative.

Question 3
A escalator is moving downwards with a uniform speed u. A man of mass m is running upwards on it at a uniform speed v. If the height of escalator is h, the work done by man in going up the escalator is

(a) zero

(b) mgh

(c) mghu/(v-u)

(d) mghv/(v-u)

Question 4

A particle moves in a circular orbit with a uniform angular speed. However , the plane of the circular orbit is itself rotating at a constant angular speed. We may then say that

(a) the angular velocity as well as angular acceleration of particle are both constant.

(b) neither the angular velocity nor the angular acceleration of the particle are constant.

(c) the angular velocity of the particle varies but its angular acceleration is constant.

(d) the angular velocity of the particle remains constant but the angular acceleration varies.

 

Question 5

Two objects of mass m and 4m are at rest at infinite separation. They move towards each other under mutual gravitational attraction. Then at separation r, which one of the following is true.

(a) the total energy of the system is not zero

(b) the force between them is not zero

(c) the center of mass of the system is at rest

(d) all the above are true

Answer
1. b
2. d

3. d

4. c

5. d

 

Multiple choice question with one or more answer

1. Which of these is true of a conservative force?
a. Workdone between two points is independent of the path
b. Workdone in a closed loop is zero
c. if the workdone by the conservative is positive,its potential energy increases
d. None of the these

2.A particle is acted upon by a force of costant magnitude which is always perpendicular to the velocity of the particle.The motion of the particle takes place in a plane.it follows that
a. velocity is constant
b. accelerattion is constant
c. KE is constant
d. Particle moves in a circular path

3. A package is dropped out of airplane in a level flight.If air resistance could be neglected.which of these is true
a. Package will follow a parabolic path with respect to a observer on the groud
b Package will follow a vertically straight line path with respect to the observer in the plane.
c.Package will follow a vertically straight line path with respect to a observer on the groud
b Package will follow a parabolic path with respect to the observer in the plane.


4.A small mass m is suspended from one end of a vertical string. and then whirled in a horizontal circle at a constant speed v.
Which of the followings is true
a.The strings stays vertical
b.The string becomes inclined to the vertical.
c.There is no force on mass m except its weight
d.The angle of inclination of the string does not depend on the v
e.The centripetal force on m is mg

5.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.Which of the following is true for the forces R_{ground->table} and R_{table->ground}
a. It is action and reaction pair
b. have equal magnitude
c. Opposite direction
d.have resultant zero


6.The tension in cable supporting an elevator is equal to th weight of the elevetor.The elevator may be
a. going up with incresing speed
b. going down with increasing speed
c. going up with uniform speed
d. going down with uniform speed.


7 A simple pendulum consists of a mass attached to a light string l. if the system is oscillating through small angles which of the following is true
a.The freqiency is independent of the acceleration due to gravity g
b.The period depends on the amplitude of the ocsillation
c.the period is independent of mass m
d. the period is independent of lenght l


8.A ball is thrown into the air with an intial speed u.The time interval taken for the ball to rise to its maximum height is t₁.The time interval taken for the ball to fall back from this maximum height is t₂.Under real life condition,which of the following is satisfied
a.t₂ > t₂
b t₂ < t₂
c. t₂=t₂
d. t₁ > t₂ if u is great enough


9. Let v and a denote the velolcity and acceleratio respectivly of the particle in one dimension motion.
a.the speed of the particle decreases when v.a <0
b. the speed of the particle decreases when v.a >0
c.the speed of the particle increases when v.a=0
d. the speed of the particle decreases when |v|<|a|

10. A refrence frame attached to the earth
a.is an inertial frame by defination
b.cannot be inertial frame as earth is resolving around the sun
c.is an intertial frame because Newton's law are applicable in this frame
d.cannot be intertial frame because earth is rotating about its own axis


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

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 

 

 

 

 

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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 

Test Yourself

1. A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement x is proportional to
(a) x²
(b) e^x
(c) x
(d) log_e x

2. Which of the following statements is false for a particle moving in a circle with a constant angular speed.
(a) The velocity vector is tangent to the circle
(b) the acceleration vector is tangent to the circle
(c) the acceleration vector points to the centre of the circle
(d) the velocity and acceleration vectors are perpandicular to each other

3. If A × B = B × A, then angle between both the vectors is
(a) π
(b) π/3
(c) π/2
(d) π/4

4. A ball is released from top of the tower of hight h m. It takes t sec. to reach the ground. What is the position of ball in T/3 sec.
(a) h/9 m from the ground
(b) 7h/9 m from the ground
(c) 8h/9 m from the ground
(d) 17h/18 m from the ground

5. A machine gun fires a bullet of mass 40g with a velocity 1200 m/s. the man holding it can exert a maximum force 144 N on the gun. How many bullets can he fire per second at the most.
(a) one
(b) four
(c) two
(d) three

Answer
1. a
2. b
3. a
4. c
5. d



Qiestion 1
If relatibe permeability of iron is 5500 then its magnetic susceptibility is
(a) 5500 x 10⁷
(b) 5501
(c) 5499
(d) 5500 x 10^-7

Question 2
An atom is paramagnetic if it has
(a) an electric dipole moment
(b) no magnetic moment
(c) a magnetic moment
(d) no electric dipole moment

Question 3
Magnetic moment of a diamegnetic atim is
(a) 0
(b) infinity
(c) negative
(d) positive

Question 4
Mark the correct statement(s)
(a) When a particle moves under uniform circular motion its acceleration is constant
(b) Under the influence of uniform circular motion , instantaneous acceleration is perpandicular to the tangential velocity
(c) Under the influence of non-uniform circular motion , instantaneous acceleration is perpandicular to the tangential velocity
(d) All the above

Qiestion 5
In a meter bridge apparatus , the bridge wire should have
(a) high resistivity and low temperature coefficent
(b) high resistivity and high temperature coefficent
(c) low resistivity and high temperature coefficent
(d) low resistivity and low temperature coefficent

Question 6
Mark out the correct statement
(a) Image formed by convex mirror can be real
(b) Image formed by convex mirror can be virtual
(c) Image formed by convex mirror can be magnified
(d) Image formed by convex mirror can be inverted

Answer
1. c
2. c
3. a
4. b .... When a particle moves under the influence of uniform circular motion magnitude of acceleration is always constant but direction of acceleration keeps changing, it always remains towards the centre . So acceleration is always perpandicular to the the tangential velocity in this case.
5. a
6. a,b,c,d 



Given below are the questions you can prepare for IITJEE-2011, AIEEE-2011 and PMT-2011 examinations. Few questions from the questions given below have been aske in previous year IITJEE, AIEEE and other such exams.

Question 1. Three capacitors of 8μF , 12μF and 24μF are connected (A) in series combination and then (B) in parallel combination . The ratio of equivalent capacitance in case (B) to that of case (A) is
(a) 11:1
(b) 1:11
(c) 1:1
(d) 3:1

Question 2. A piece of copper and a piece of germanium are cooled from the room temperature down to 80K
(a) resistance of each of them increases
(b) resistance of each of them decreases
(c) resistance of copper increases and that of germanium drcresaes.
(d) resistance of copper decreases and that of germanium increases.

Question 3. A current flows along the length of infinitely -long straight , thin walled pipe then,
(a) magnetic field at all points inside the pipe is same , but non zero
(b) the magnetic field at any point inside the pipe is zero.
(c) magnetic field is zero only on the axis of the pipe
(d) magnetic field is different at different points inside the pipe

Question 4. The line on the earth's surface joining the points where the field is horizontal is called
(a) magnetic maredian
(b) magnetic axis
(c) isogonic line
(d) magnetic equator

Question 5. The principle used in the transmission of signal through an optical fibre is
(a) total internal reflection
(b) reflection
(c) refraction
(d) dispersion

Question 6. Milikan's oil drop experiment established that
(a) electric charge depends on velocity
(b) electron has wave nature
(c) electron has particle nature
(d) electronic charge is quantized

Question 7. For steady direct current to flow in a circuit
(a) circuit must contain a source of emf
(b) charge distribution in circuit must remain unchanged
(c) lines of current density vector are closed one
(d) all of the above

I hope that these question answes will help you prepare physics for IITJEE, AIEEE and PMT exams

Answer:-
1. (a)
2. (d)
3. (b)
4. (d)
5. (a)
6. (d)
7. (d)

Question 1:A gas is contained in a vertical, frictionless piston cylinder device. The piston has a mass of 20 kg with a cross-sectional area of 20 cm² and is pulled with a force of 100N. If the atmospheric pressure is 100 kPa, determine the pressure inside.


Question 2:A piston-cylinder device has a ring to limit the expansion stroke. Initially the mass of Oxygen is 2 kg at 500 kPa, 30° C. Heat is now transferred until the piston touches the stop, at which point the volume is twice the original volume. More heat is transferred until the pressure inside also doubles. Determine the amount of heat transfer and the final temperature.


Question 3: A piston cylinder device contains 1 kg of oxygen at 150 kPa, 30°C. The cross-sectional area of the piston is 0.1 m². Heat is now added causing gas to expand. When the volume reaches 0.2 m³, the piston reaches a linear spring with a spring constant of 120 kN/m. More heat is added until the piston rises another 25 cm. Determine the final pressure, temperature and the energy transfers.


Question 4:Is the energy of the system U an intensive or extensive variable?



Question 5:Suppose we have M+N systems prepared, and the first is in thermal equilibrium with the second, the second in thermal equilibrium with the third, etc., until system M+N- 1 is in thermal equilibrium with the M+Nth system. Is the first system in thermal equilibrium with the M+Nth?


Question 6:A gas is contained in a cylinder with a moveable piston on which a heavy block is placed. Suppose the region outside the chamber is evacuated and the total mass of the block and the movable piston is 102 kg. When 2140 J of heat flows into the gas, the internal energy of the gas increases by 1580 J. What is the distance s through which the piston rises?


Question 7:A resistance thermometer is such that resistance varies with temperature as
R_T=R₀(1+aT+bT⁵)
where T represent Temperature on Celsius scale And a,b,R₀ are constants.R₀ unit is ohm
Based on above data ,Find out the unit of a,b


Solution 1:
Total forces on the piston
Weight of the piston acting downward=200N
Force due to Atmospheric pressure downward =100*10³*20*10^-4 N=200N
Let P be the Pressure of the gas
Then Force acting due to pressure of gas on the piston upward=PA
Force with the piston is being pulled upward=100N

Total Upward force=Total Downward force
PA + 100=200 +200
20*10^-4*P=300
P=150kPa

Solution 2:

Since O₂ is a diaatomic gas
C_P=7R/2,C_V=5R/2
Molecular mass=32 gm

Intial state
Intial volume of gas
V=nRT/P
n=2*10³/32
T=303K
R=8.3
P=500*10³ N/m²
so V=.314 m³

Second state when At top volume becomes double

Volume=2*.314 =.628m³
Pressure=500*10³ N/m² remains same

So as per ideal gas equation
T=606K

Workdone by the gas=PV=500*10³*.314=157*10³ J
Heat transfered=nC_P(T₂ -T₁)
=2*10³ *7*8.3*303/32*2
=550*10³ J

Third state when Pressure becomes double
P=1000*10³ N/m²
V=.628m³

As per ideal gas equation
Temperature=1212K
Heat transfered=nC_V(T₃ -T₂)
=2*10³ *5*8.3*606/32*2
=785 kJ

So total heat tranfered=550+785=1335 kJ
Final Temperature=1216 K

Solution 3:
Since O₂ is a diaatomic gas
C_P=7R/2,C_V=5R/2
Molecular mass=32 gm

Intial state
Intial volume of gas
V=nRT/P
n=1*10³/32
T=303K
R=8.3
P₀=500*10³ N/m²
so V=.157 m³

Second state ( when piston reaches the spring)
v=.2 m³
P=500*10³ N/m²
As per ideal gas equation
Temperature becomes=385.5 K


So heat tranfer till that point=nC_P(T₂ -T₁)
=1*10³ *7*8.3*82.5/32*2
=74.8 KJ

Third state ( when it compresses the spring)V=.2+0.1*0.25=0.225 m³
P=500*10³ + kx/A
=500*10³ + 120*10³*25*10^-2/.1
=800*10³ N/m²

As per ideal equation
Temperature becomes=694K
Change in Internal energy=nC_V(T₃ -T₂)=5nR(T₃ -T₂)/2
=5*1*10³*8.3*308.5/32*2
=200 KJ

Workdone by the gas =P₀Ax + kx²/2
=500*10³*.1*.25 + 120*10³*.25*.25/2
=16.25 KJ

Total heat supplied in this Process=200+16.25=216.25KJ

So net Heat transfer=291.05 KJ

Solution 4:
Doubling the system should double the energy, so U is an extensive variable.


Solution:5
By repeated application of the Zeroth Law, we can state that all M+N systems are in thermal equilibrium with each other.

Solution:6

Total heat supplied =Workdone + Change in internal energy

So work done=2140-1580=560 J

Let s be the distance moved then
the workdone is given by =Fs
Fs=560
s=560/F
=560/102*10
s=.54 m

Solution:7
As per dimension analysis Unit on both sides should be equal
Now since R & R₀ both unit are same
Quantity 1+aT+bT⁵ should be dimension less
so at should be dimension less
so a unit is C^-1
similarly bt⁵ should be dimensionless
so b unit is C^-5

 

IITJEE previous year questions

Question 1
A particle executes SHM with frequency f. The frequency with which its Kinetic energy oscillates is
(a) f/2
(b) f
(c) 2f
(d) 4f

Question 2
A linear harmonic oscillator of force constant 2 x 10⁶N/m and amplitude 0.01 m has a total mechanical energy of 160J. Its
(a) Maximum potential energy is 100J
(b) Maximum kinetic energy is 100J
(c) Maximum potential energy is 160J
(d) Minimum potential energy is zero

Question 3
A given quantity of ideal gas is at pressure P and absolute temperature T. The isothermal bulk modulus of gas is
(a) 2P/3
(b) P
(c) 3P/2
(d) 2P

Question 4
During the melting of slab of ice at 273K at atmospheric pressure
(a) positive work is done by the ice water system on the atmosphere
(b) positive work is done on the ice water system by the atmosphere
(c) the internal energy of the ice water system increases
(d) the internal energy of the ice water system decreases


Question 5
When an ideal diatomic gas is heated at a constant pressure , the fraction of the heat energy supplied which increases the internal energy of the gas is
(a) 2/5
(b) 3/5
(c) 3/7
(d) 5/7
 
Question 6
In a given process on an ideal gas , dW=0 and dQ<0. then for the gas
(a) the temperature will decrease
(b) the volume will increase
(c) the pressure will remain constant
(d) the temperature will increase

Question 7
A cylinder rolls up an inclined plane, reaches some hight, and then rolls down (without slipping through these motions). The directions of frictional force acting on the cylinder are
(a) up the incline while ascending and down the incline descending
(b) up the incline while ascending as well as descending
(c) down the incline while ascending and up the incline while descending
(d) down the incline while ascending as well as descending
 
 

Answer
1. c
2. c,d
3. b
4. b,c
5. d
6. a
7. b

IITJEE physics questions

1. c
2. c
3. c

4. a
5. b Mutual inductance of pair of coils depends on relative position and orientation of the two coils. This is in addition to other factors not given in the alternatives.
6. b use P=P₁+P₂ where p is total power of combination of lenses
7. d

mechanics test questions

Question 1
A ball is thrown vertically upwards with a velocity u from top of a tower. It strikes the ground with a velocity 3u. The time taken by the ball to reach the ground is given by
(a) u/g
(b) 2u/g
(c) 3u/g
(d) 4u/g

Question 2
A body slides down an inclined plane of inclination . The coefficient of friction down the plane varies in the direct proportion to the distance moved down the plane(=kx). The body will move down the plane with
(a) constant acceleration =gsin
(b) constant acceleration =(gsin-gcos)
(c) constant retardation =(gcos-gsin)
(d) variable acceleration that first decreases from gsin to zero and that becomes negative.

Question 3
A escalator is moving downwards with a uniform speed u. A man of mass m is running upwards on it at a uniform speed v. If the height of escalator is h, the work done by man in going up the escalator is

(a) zero

(b) mgh

(c) mghu/(v-u)

(d) mghv/(v-u)

Question 4

A particle moves in a circular orbit with a uniform angular speed. However , the plane of the circular orbit is itself rotating at a constant angular speed. We may then say that

(a) the angular velocity as well as angular acceleration of particle are both constant.

(b) neither the angular velocity nor the angular acceleration of the particle are constant.

(c) the angular velocity of the particle varies but its angular acceleration is constant.

(d) the angular velocity of the particle remains constant but the angular acceleration varies.

 

Question 5

Two objects of mass m and 4m are at rest at infinite separation. They move towards each other under mutual gravitational attraction. Then at separation r, which one of the following is true.

(a) the total energy of the system is not zero

(b) the force between them is not zero

(c) the center of mass of the system is at rest

(d) all the above are true

Answer
1. b
2. d

3. d

4. c

5. d

 

 

Problem on Bohr atom model

 

Question:
A particle of charge equal to that of electron and mass 208 times the mass of electron (-meson)moves in a circular orbit around a nucleus of charge +3e (assume mass of nucleus to be infinite). Assuming that the Bohr atom model is applicable to this system
(a) derive an expression for the radius of the nth Bohr orbit
(b) find the value of n for which the radius of the orbit is approximately the same as that of the first Bohr orbit for the hydrogen atom
(c) find the wavelength of the radiation emitted when  -meson jumps from the third orbit to the first orbit (Rydberg constant = 1.097 x 107 m-1)  

Question:

A particle of charge equal to that of electron and mass 208 times the mass of electron moves in a circular orbit around a nucleus of charge +3e (assume mass of nucleus to be infinite). Assuming that the Bohr atom model is applicable to this system

(a) derive an expression for the radius of the nth Bohr orbit

(b) find the value of n for which the radius of the orbit is approximately the same as that of the first Bohr orbit for the hydrogen atom

(c) find the wavelength of the radiation emitted when   jumps from the third orbit to the first orbit (Rydberg constant = 1.097 x 107 m-1)  

Solution

(a) Let M be the mass of the  and q be its charge. The centripetal force of the circular motion  of  is provided by the Coulomb attraction between the nucleus and  i.e..

                     (1)

where v is the speed of the in the n th Bohr orbit of radius .

                      (2)

According to the Bohr postulate, the angular momentum of is an integral multiple of , i.e.,

                                (3)

eliminating v from 2 and 3 we get

putting q=e , Q=3e , and M=208m where m is the mass of the electron then

                               (4)

(b) The radius of the first Bohr orbit is

On equating it equal to equation 4 we find

(c) The total energy of in the nth permitted orbit is

 using equation 1

Substituting the value of  from equation 4 we get

where is the Rydberg constant whose value is given in the  question.

When jumps from third orbit to the first orbit , the energy if emitted radiation is

The wavelength of the radiation is given by

calculating for wavelength we get

 

 

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