Two billiard balls A and B, each of mass 50g and moving in opposite directions with a speed of 5 m/s each, collide and rebound at the same speed. If the collision lasts for 10-3 s,

(a) The impulse imparted to each ball is 0.25 kgms1 and the force on each ball is 250 N

(b) The impulse imparted to each ball is 0.25 kgms1 and the force exerted on each ball is 25 x 10-N

(c) The impulse imparted to each ball is 0.5 N-s

(d) The impulse and the force on each ball are equal in magnitude and opposite in direction.

Which of the following statement(s) is/are true?

1. (a, c)

2. (a, b)

3. (c, d)

4. (b, c)

Subtopic:  Collisions |
 68%
From NCERT
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Two blocks \(M_1\)​ and \(M_2\)​ having equal mass are free to move on a horizontal frictionless surface. \(M_2\)​ is attached to a massless spring as shown in figure. Initially, \(M_2​\) is at rest and \(M_1​\) is moving toward \(M_2\)​ with speed \(v \) and collides head-on with \(M_2.\) 

      
Consider the following given statements:

(a). while spring is fully compressed, all the kinetic energy of \(M_1​\) is stored as potential energy of spring.
(b). while spring is fully compressed, the system's momentum is not conserved, though final momentum is equal to initial momentum.
(c). if spring is massless, the final state of the \(M_1\) is state of rest.
(d). if the surface on which blocks are moving has friction, then collision cannot be elastic.
Choose the correct option:
1. only (a)
2. (a), (b)
3. (b), (c)
4. (c), (d)
Subtopic:  Collisions |
From NCERT
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A body of mass \(0.5\) kg travels in a straight line with velocity \(v=ax^{3/2}\) where \(a=5~\mathrm{m^{-1/2}s^{-1}}\). The work done by the net force during its displacement from \(x=0\) m to \(x=2\) m is:
1. \(15\) J
2. \(50\) J
3. \(10\) J
4. \(100\) J

Subtopic:  Work Done by Variable Force |
 67%
From NCERT
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Two identical ball bearings in contact with each other and resting on a frictionless table is hit head-on by another ball bearing of the same time moving initially with a speed \(v\) as shown in the figure.

 

If the collision is elastic, which of the following (figure) is a possible result after collision?

1. 2.
3. 4.
Subtopic:  Collisions |
 79%
From NCERT
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The potential energy function for a particle executing linear SHM is given by V(x)=12kx2 where k is the force constant of the oscillator (Fig). For k = 0.5 N/m, the graph of V(x) versus x is shown in the figure. A particle of total energy E turns back when it reaches x=±m. If V and K indicate the PE and KE, respectively of the particle at x=+m, then which of the following is correct?



1. V=0, K=E
2. V=E, K=0
3. V<E, K=0
4. V=0, K,E

Subtopic:  Elastic Potential Energy |
 71%
From NCERT
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Two inclined frictionless tracks, one gradual and the other steep meet at \(A\) from where two stones are allowed to slide down from rest, one on each track as shown in the figure.

Which of the following statement is correct?

        

1. Both stones reach the bottom at the same time but not at the same speed.
2. Both the stones reach the bottom with the same speed and stone I reaches the bottom earlier than stone II.
3. Both the stones reach the bottom with the same speed and stone II reaches the bottom earlier than stone I.
4. Both stones reach the bottom at different times and at different speeds.



 

Subtopic:  Gravitational Potential Energy |
 62%
From NCERT
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During an inelastic collision between two bodies, which of the following quantities always remain conserved?

1. total kinetic energy         
2. total mechanical energy
3. total linear momentum   
4. speed of each body
Subtopic:  Collisions |
 81%
From NCERT
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A body is falling freely under the action of gravity alone in a vacuum. Which of the following quantities remain constant during the fall?

1. kinetic energy
2. potential energy
3. total mechanical energy
4. total linear momentum

Subtopic:  Gravitational Potential Energy |
 81%
From NCERT
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A bicyclist comes to a skidding stop in \(10\) m. During this process, the force on the bicycle due to the road is \(200\) N is directly opposed to the motion. The work done by the cycle on the road is:
1. \(+2000\) J
2. \(-200\) J
3. zero
4. \(-20000\) J

Subtopic:  Work done by constant force |
 58%
From NCERT
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A man squatting on the ground gets straight up and stands. The force of reaction of the ground on the man during the process is

1. constant and equal to mg in magnitude.
2. constant and greater than mg in magnitude.
3. variable but always greater than mg.
4. at first, greater than mg and later becomes equal to mg.

Subtopic:  Concept of Work |
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