Match the scenarios involving collisions with the correct outcome or related quantity. List - I List - II (P) A particle of mass m moving with velocity v collides elastically and head-on with an ident

Question

Match the scenarios involving collisions with the correct outcome or related quantity.

List - I	List - II
(P) A particle of mass $m$ moving with velocity $v$ collides elastically and head-on with an identical particle at rest. The velocity of the first particle after collision is...	(1) $0$
(Q) A particle of mass $m$ moving with velocity $v$ collides inelastically and head-on with an identical particle at rest. If they stick together, the velocity of the combined mass is...	(2) $v /2$
(R) Two masses $m_{1}$ and $m_{2}$ collide head-on. If $e$ is the coefficient of restitution, the relative velocity of separation is...	(3) $e (u_{1} - u_{2})$
(S) A ball dropped from height $h$ rebounds to height $h^{'}$ . The coefficient of restitution is...	(4) $h^{'} / h$

TestHub · Accepted Answer

For P, in a 1D elastic collision of identical masses where one is at rest, they exchange velocities. So, the first particle stops ( v 1 ′ ​ = 0 ). For Q, by momentum conservation, m v = ( m + m ) V f ​ , so V f ​ = v /2 . For R, the definition of coefficient of restitution is e = ( v 2 ′ ​ − v 1 ′ ​ ) / ( u 1 ​ − u 2 ​ ) , so the relative velocity of separation is e ( u 1 ​ − u 2 ​ ) . For S, e = h ′ / h ​ relates the heights before and after rebound.

Physics - Center of Mass Question with Solution | TestHub

Options:

Doubts & Discussion