Test: 35 Year JEE Previous Year Questions: Momentum and Impulse - JEE MCQ

Statement 1 : For an elastic collision, the coefficient of restitution = 1

⇒ Relative velocity after collision is equal to relative velocity before collision. But in the statement relative speed is given.
Statement 2 : Linear momentum remains conserved in an elastic collision. This statement is true

Let n  be the number of bullets that the man can fire in one second.
∴ change in momentum per second = n x mv = F
[m = mass of bullet, v = velocity]  (∵ F is the force)

In x-direction,  mv = mv₁ cosθ ...(1) where v₁ is the velocity of second mass

In y-direction, 

Squaring and adding eqns. (1) and (2)

Let the velocity and mass of 4 kg piece be v₁ and m₁ and that of 12 kg piece be v₂ and m₂

Applying conservation of linear momentum

In completely inelastic collision, all energy is not lost (so, statement -1 is true) and the principle of conservation of momentum holds good for all kinds of collisions (so, statement -2 is true) . Statement -2 explains statement -1 correctly because applying the principle of conservation of momentum, we can get the common velocity and hence the kinetic energy of the combined body.

During each collision

Impulse  = Change in momentum

Statement II is a case of perfectly inelastic collision.
By comparing the equation given in statement I with above equation, we get

Hence statement I is wrong and statement II is correct.

Initial momentum of the system

Final momentum of the system = 3mV By the law of conservation of momentum

Percentage loss in energy during the collision = 56%