IIT JAM Physics MCQ Test 2


30 Questions MCQ Test Mock Test Series for IIT JAM Physics | IIT JAM Physics MCQ Test 2


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This mock test of IIT JAM Physics MCQ Test 2 for Physics helps you for every Physics entrance exam. This contains 30 Multiple Choice Questions for Physics IIT JAM Physics MCQ Test 2 (mcq) to study with solutions a complete question bank. The solved questions answers in this IIT JAM Physics MCQ Test 2 quiz give you a good mix of easy questions and tough questions. Physics students definitely take this IIT JAM Physics MCQ Test 2 exercise for a better result in the exam. You can find other IIT JAM Physics MCQ Test 2 extra questions, long questions & short questions for Physics on EduRev as well by searching above.
QUESTION: 1

A bullet of mass m moving with a horizontal velocity n strikes a stationary block of mass M suspended by a spring of length L. The bullet gets embedded in the block. Prove that the maximum angle made the string after impact is 

Solution:

The situationn is shown in figure. Let n' be the velocity of the block with the embedded bullet after impact.
Applying the law of conservation of momentum, i.e.,

Momentum before impact = Momentum after impact
mn = (M + m)n'......(1)
Applying the law of conservation of mechanical energy, i.e., K.E. of the combined mass = P.E. at the highest point 
 .....(2)
From figure,
h = L -L cosq = L(1-cosq).
From equations (2) and (3), we get
 ....(4)
Substituting the value of n' from equation (1), we get

or 


 

QUESTION: 2

A sphere has a perfectly elastic oblique collision with another identical sphere which is initially at rest. The angle between their velocities after the collision is

Solution:

Law of conservation of momentum gives
mu1 = mv1cosq1 + mv2cosq2 .......(1)
and 0 mv1sinq1 - mv2sinq1 ....(2)

Energy conservation gives
 ....(3)
Squaring and adding (1) and (2) and comparing with (3) we get θ1 + θ2 = 90o

QUESTION: 3

A girl throws a ball with initial velocity u at an inclination of 45o. The ball strikes the smooth vertical wall at a horizontal distance d from girl and after rebounding returns to her hand. What is the coefficient of restitution between wall and ball?

Solution:


As the wall is smooth, the vertical component of the impulse it receives is zero. The total time of flight is given by

The time of flight t1 from G to A = 
The time of flight l2 from A to G = 
where e = coefficient of restitution.


Solving we get e = 

QUESTION: 4

A uniform chain of mass m and length I hangs on a thread and touches the surface of a table by its lower end. Find the force exerted by the table on the chain when half of its length has fallen on the table. The fallen part does not form heap.

Solution:

Weight of the portion BC of the chain lying on the table, W = mg/2(downwards)
Thrust force 


F1 = lv(where, λ = m/l, is mass per unit length of chain)

 (downwards)
Net force eerted by the  chain on the table is 

So, from Newton's thrid law the force exerted by the table on the chain will be 3/2 mg (vertically upwards).

QUESTION: 5

It l1 , l2 and l3 are the moments of inertia about, a diameter of a thin hollow sphere, solid sphere and disc having same mass and same radius respectively, then which one of the following is correct?

Solution:




where
m = mass
r = radius
clearly 
⇒ I1>I3>I2

QUESTION: 6

A uniform rod of length l is free to rotate in a vertical plane about a fixed horizontal axis through B. The rod begins rotating from rest from its unstable equilibrium position. When  it has turned through an angle q, its angular velocity w is given as

Solution:


When the rod rotates through an angle q, the centre of gravity falls through a distance h from DBG'C,

 ..(1)
The decrease in P.E. is equal to the kinetic energy of rotation 
 ...(2)
From equation (1) and (2), we get 

QUESTION: 7

Two bodies with moment of inertia l1 and l2 and (l1>l2) have equal angular momenta. If K.E. of rotation are E1 and E2 then

Solution:


 ...(i)

or  ...(ii)
Frin eqs, (1) and (2), we get

QUESTION: 8

The object in Figure might be a billiard ball a steel ball bearing, or the world's largest ball of string. Find the moment of the inertia about an axis through the center of the sphere.

Solution:

We divide the sphere into thin disks of thickness dx. The radius r or the disk shown is 

Its volume is 
dV = pr2   dx = p(R2-x2)dx
and its mass is 
dm = r dV = pr (R2-x2) dx

We will find the moment of inertia of a sphere about an axis through its center 
The mass element is a disk with thickness dx.
The moment of inertia of a disk of radius r and mass dm is 

Integrating this expression from x = 0 to x = R gives the moment of inertia of the light hemisphere. From symmetry, the total I for the entire sphere is just twice of this: 

Carrying out the integration, we obtain

The mass M of the sphere of the volume V = 4pR3/3 is 

By comparing the expression for I and M, we find

QUESTION: 9

Figure shows a hollow, uniform cylinder with length L, inner radius R1, and outer radius R2, It might be a steel cylinder in a printing press or a sheet- steel rolling mill. The moment of inertia about the axis of symmetry of the cylinder is,

Solution:

We choose a thin cylindrical shell of radius r, thickness dr, and length L as a volume element. All parts of this element are at very nearly the same distance from the axis. The volume of the element is very nearly equal to that of a flat sheet with thickness dr, length L, and width 2pr(the circumference of the shell).
Then
dm = p dV = p (width x length x thickness)
= r(2prL dr) .....(1)

The moment of inertia is given by
 [use equation(1)]


If we express the moment of inertia in terms of the total mass M of the body. 
Then
 Q m = rV ......(3)
and the volume of the cylindrical shell is 
 [Volume of the cylinder V = pR2h] ...(4)
From equation (3) and (4) we get 
 ...(5)
using equation (5) in equation (2), we get

QUESTION: 10

Moment of inertia of a solid cylinder of mass M height 2h  and radius 2r about an axis (shown in the figure by dahsed line) passing through its centre of mass and perpendicular to its symmetry axis is 

Solution:


Let radius & height of solid cylinder is 2r and 2h. Assume that it is made up by small disc having radius 2r. Now we take a disc of width of dx and at x distance from zz' axis volume of thin disc is = π(2r)2dx
so, mass dm = 
where    is mass per unit volume
so moment of inertia about the diameter AB is 

By theorem of "parallel axes"  moment of inertia w.r.t. axis xz is 


So, Total moment of inertia,

QUESTION: 11

Consider the following statements with reference to X-rays: 
1. They produce heat when absorbed by matter. 
2. They are generated when fast-moving electrons strike a metal target. 
3. They can penetrate through a thin sheet of aluminium. 
Which of the statements given above are correct?

Solution:

The following statements are reference to X-rays: 
1. They produce heat when absorbed by matter : X-ray beam attenuation. As the x-ray beam passes through tissue, photons get absorbed so there is less energy; this is known as attenuation. It turns out that higher energy photons travel through tissue more easily than low-energy photons (i.e. the higher energy photons are less likely to interact with matter). 
2. They are generated when fast-moving electrons strike a metal target : An electromagnetic wave called x-ray is produced when fast moving electrons impact on high atomic weight substances. However, when these fast moving electrons strike on a metal target, a photoelectric effect occurs. 
3. They can penetrate through a thin sheet of aluminium : X-Rays will Pass Straight through Aluminium of Almost ANY Thickness as it's Density is so Low !! But the Crystalline Structure of Diamond makes it Totally Opaque to X-Rays !! X-Rays do not "see"! But yes, they can pass easily through a single sheet of aluminum foil.

QUESTION: 12

An elastic collision conserves.

Solution:

 We know that in elastic collision both kinetic energy and momentum remains conserved.

QUESTION: 13

Two particles A and B initially at rest, moves towards each other under a mutual force of attraction. If at an instant the speed of A is V and that of B is 2V then the speed of the centre of mass of the system is 

Solution:

According to principle of Conservation of momentum under mutual attractive force. The momentum of centre of mass remains constant, since the system is initially at rest, hence is momentum is zero.

QUESTION: 14

Radioactive  decays into  by emitting a positron and a neutrino. The positron and the neutrino are observed t move at right angles to each other and carry momenta 2 x 10-22 and 5 x 10-23 kg  msec-1 respectively. Then the momentum of the recoiling nucleus is 

Solution:

Let the positron more along the +ve x-direction and the neutrino along +y direction with momenta 

QUESTION: 15

A uniform chain of mass m and length I hangs on a thread and touches the surface of a table by its lower end. find the force exerted by the table on the chain when half of its length has fallen on the gable. The fallen part does not from heap.

Solution:

Weight of the portion BC of the chain lying on the table W = mg/2 (downwards)
Thrust force 

 is mass per unit length of chain 


Net force exerted by the chain on the table is 

So, from Newton's third law the force exerted by the table on the chain will be 
3/2 mg (vertically upwards)

*Multiple options can be correct
QUESTION: 16

Two objects of masses m1 = 200 gm and m2 = 500gm possess velocities  just prior to a collision during which they become permanently attached to each other.

Solution:


(b) Final momentum =  (m1+m2) V = 0.7V =

Now applying the law of conservation of momentum

where v is the velocity of the combined particle in the laboratory system. Note that v is identical to V, i.e.,   
Therefore 
Thus 

*Multiple options can be correct
QUESTION: 17

A particle is released at x = 1 in a force field  which one of the following statement is true?

Solution:



Since,  is exact differential work done by this force is independent of path. So the force is conservative
Torque about origin is zero, so angular momentum of particle is constant about origin.
Equilibrium position of particle is given by
F(n) = 0


 
 so potential energy is minimum at x = 3 1/3
So, x = 3 1/3 is point of stable equilibrium.
Hence, the particle will move towards x = 1

*Multiple options can be correct
QUESTION: 18

A particle is acted upon by a force  Which of the following statements are false?

Solution:

If a force or a vector quantity is conservative the 


And if  is conservative then a scalar potential v exist such that 

⇒ v = -xyz

*Multiple options can be correct
QUESTION: 19

The stream function  of two dimensional flow field is given by 

Solution:

Stream function ψ is given by

Equation of streamline is given by

where u and v are velocity components of fluid velocity 

So, velocity of fluid

The flow is irrotational if 


Since,  the velocity of fluid  can be expressed as gradient of scaler potential 

*Multiple options can be correct
QUESTION: 20

A container of large uniform cross-sectional area A resting on a horizontal surface has two immiscible, non-viscous and incompressible liquids of densities d and 2d, each of height H/2 as shown. The lower density liquid is open to the atmosphere having pressure P0. A tiny hole of area s(s<<A) is punched on the vertical side of the container at a height h (h < H/2). Determine: 

Solution:

Here the effective height of orifice cannot be taken as (H-h) due to the presence of two liquids. Using Berrnoulli,s theorem just inside and just outside the orifice, we have


where V is the velocity of efflux


...(i)
2. Let be the time taken by the liquid to hit the ground. Then
....(ii)
The horizontal range x = Vt
 [use equation (1) and (2)]

...(iii)
3. Q 
Differentiate x with respect to h and equate it to zero for maximum h.



Value of h put in equation(3)

*Answer can only contain numeric values
QUESTION: 21

At what time a Foucault's pendulum completes a round when it is at 450N latitude on north pole?


Solution:

The period of oscillation of Foucalt's pendulum at the place of latitude is given as 

at l = 450

*Answer can only contain numeric values
QUESTION: 22

An astronaut travelling in a rocket moving vertically upwards with an acceleration of 4g weighs 300kg. Then find out the weight (in Kg) of the astronaut in the laboratory.


Solution:

The apparent weight is given by 

Taking downward direction positive, the force in vertically upward direction is 
F = mg + ma0



Therefore the weight of the astronaut in the aboratory is 60kg.

*Answer can only contain numeric values
QUESTION: 23

A solid sphere of mass 2m and radius a/2 is rolling with a linear speed v on a flat surface without slipping. The magnitude (in mav) of the angular momentum of the sphere w.r.t. a point along the path of the sphere on the surface is....


Solution:

A solid sphere is rolling along the flat surface without slipping and p is the point on the surface of sphere.
So, angular momentum of sphere about P is L = 2mv * a/2

*Answer can only contain numeric values
QUESTION: 24

A bullet of mass 10 g. is fired with a speed of 1,000 m/s. from a freely hanging gun of mass 2 kg. Calculate the recoil velocity of gun (in m/s).


Solution:

The initial momentum of the system (gun + bullet) = 0
Final momentum of the system = m1n1 + m2n2
where m1 and m2 are the masses of the gun and bullet respectively and n1 and n2 are their velocities finally.
According to principle of conservation of linear momentum.
Initial momentum = Final momentum



The gun will move in opposite direction to that of the bullet with velocity 5 m/s.

*Answer can only contain numeric values
QUESTION: 25

Two skaters collide and embrace, in a completely in elastic collision. That is they stick together after impact, as suggested by figure, where the origin is placed at the point of collision. Alfred, whose mass mA is 83 kg, is originally moving east with speed nA = 6.2 km/h. Barbara, whose mass mB is 55 kg is originally moving north with speed nB = 7.8 km/h.

What is the velocity (km/hr) v of the couple after impact?


Solution:

Linear momentum is conserved during the collision. We can write, for the linear momentum components in the x and y directions,

in which M = mA + mB. Dividing equation (2) by equation (1) yields

Thus

From equation (2) we then have

*Answer can only contain numeric values
QUESTION: 26

A block of mass 0.18 kg is attached to a spring of force constant 2 N/m. The coefficient of friction between the block and the floor is 0.1. Initially, the block is at rest and the spring is un-stretched. An impulse is given to the block as shown in the figure. The bock slides a distance of 0.06m and comes to rest for the first time. The initial velocity of the block in m/sec is V = N/10. Then N is....


Solution:

It is given that the block slides a distance of 0.06m and comes to the rest for the first time.
μ = 0.1
By the energy conservation


*Answer can only contain numeric values
QUESTION: 27

A bob of mass m, suspended by a string of length l1, is give a minimum velocity required to complete a full circle in the verticle plane. At the highest point, it collides elastically with another bob of mass m suspended by a string of length l2, which is initially at rest. Both the strings are mass-less and inextensible. If the second bob, after collision acquires the minimum speed required to complete a full circle in verticle plane, the ration l1/l2 is ...


Solution:

To complete the vertical circle 

l1/l2 = 5

*Answer can only contain numeric values
QUESTION: 28

A ball of mass m moving at a speed v makes a head-on wllision with an identical ball at rest. The kinetic energy of the balls after the collision is 80% of the original. Find the coefficient of restilation.


Solution:

Let 



*Answer can only contain numeric values
QUESTION: 29

A rocket, with an initial mass of 3000kg, is launched vertically upwards from rest under gravity. The rocket burns fuel at the rate of 40 kg per deeond. The burnt watter is ejected vertically downwards with a speed of 4000 m/see relative to the rocket. If burning stops after one minute. Find the maximum velocity of rocket.


Solution:

We know that velocity equation is givven by 




The maximum velocity of the rodect is 
v = 4000 ln 5 - 600

= 5837.75 m/sec

*Answer can only contain numeric values
QUESTION: 30

A uniforem chain of mass m and length I hangs on a thread and touches the surface of a lable by its lower end. Find the force exerted by the table on the chain when three-founth of its length has ballen m the lable. The fallen part does not form heap.


Solution:

Weight of the portion BC of the chein 

Thrust force 


Net force exerted by the chain on the table is 

The force enerfed by the table on the chain will be 5/4 mg.

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