A bag (mass \(M\)) hangs by a long thread and a bullet (mass \(m\)) comes horizontally with velocity \(v\) and gets caught in the bag. Then for the combined (bag + bullet) system:
1. \(\text{Momentum is }\frac{mvM}{M+m}\)
2. \(\text{Kinetic energy is }\frac{mv^2}{2}\)
3. \(\text{Momentum is }\frac{mv(M+m)}{M}\)
4. \(\text{Kinetic energy is }\frac{m^2v^2}{2(M+m)}\)

A particle of mass m moving with velocity v strikes a stationary particle of mass 2m and sticks to it. The speed of the system will be 

(1) v/2

(2) 2v

(3) v/3

(4) 3v

If a skater of weight 3 kg has initial speed 32 m/s and second one of weight 4 kg has 5 m/s. After collision, they have speed (couple) 5 m/s. Then the loss in K.E. is 

(1) 48 J

(2) 96 J

(3) Zero

(4) None of these

A metal ball of mass 2 kg moving with a velocity of 36 km/h has an head on collision with a stationary ball of mass 3 kg. If after the collision, the two balls move together, the loss in kinetic energy due to collision is 

(1) 40 J

(2) 60 J

(3) 100 J

(4) 140 J

A body of mass 2kg is moving with velocity 10 m/s towards east. Another body of same mass and same velocity moving towards north collides with former and coalsces and moves towards north-east. Its velocity is 

(1) 10 m/s

(2) 5 m/s

(3) 2.5 m/s

(4) $5\sqrt{2}m/s$ 

Which of the following is not a perfectly inelastic collision 

(1) Striking of two glass balls

(2) A bullet striking a bag of sand

(3) An electron captured by a proton

(4) A man jumping onto a moving cart

A neutron having mass of $1.67\times {10}^{-27}kg$ and moving at ${10}^{8}m/s$ collides with a deutron at rest and sticks to it. If the mass of the deutron is $3.34\times {10}^{-27}kg$ then the speed of the combination is 

(1) $2.56\times {10}^{3}m/s$

(2) $2.98\times {10}^{5}m/s$

(3) $3.33\times {10}^{7}m/s$

(4) $5.01\times {10}^{9}m/s$

A body of mass m₁ is moving with a velocity V. It collides with another stationary body of mass m₂. They get embedded. At the point of collision, the velocity of the system 

(1) Increases

(2) Decreases but does not become zero

(3) Remains same

(4) Become zero

A uniform chain of length \(L\) and mass \(M\) is lying on a smooth table and one-third of its length is hanging vertically down over the edge of the table. If \(g\) is acceleration due to gravity, the work required to pull the hanging part on the table is:

1. \(MgL\)

2. \(MgL/3\)

3. \(MgL/9\)

4. \(MgL/18\)

If W₁, W₂ and W₃ represent the work done in moving a particle from A to B along three different paths 1, 2 and 3 respectively (as shown) in the gravitational field of a point mass m, find the correct relation between W₁, W₂ and W₃ 

(1) W₁ > W₂ > W₃

(2) W₁ = W₂ = W₃

(3) W₁ < W₂ < W₃

(4) W₂ > W₁ > W₃