Match the scenarios involving momentum conservation with the correct outcome or related quantity. List - I List - II (P) A block of mass M moving with velocity V 0 collides with another block of mas

Question

Match the scenarios involving momentum conservation with the correct outcome or related quantity.

List - I	List - II
(P) A block of mass $M$ moving with velocity $V_{0}$ collides with another block of mass $M$ at rest. After collision, they stick together. The final velocity of the combined mass is...	(1) $V_{0} /2$
(Q) A bomb of mass $M$ at rest explodes into two pieces of masses $M /3$ and $2 M /3$ . If the lighter piece moves with velocity $v$ , the velocity of the heavier piece is...	(2) $m_{1} v_{1} / m_{2}$
(R) A man of mass $m$ stands at one end of a boat of mass $M$ and length $L$ floating on still water. The man walks to the other end. The displacement of the boat is...	(3) $- v /2$
(S) A spring is compressed between two blocks of masses $m_{1}$ and $m_{2}$ and then released. If $m_{1}$ moves with velocity $v_{1}$ , the magnitude of the velocity of $m_{2}$ is...	(4) $m L / (M + m)$

TestHub · Accepted Answer

For P, by conservation of momentum, M V 0 ​ = ( M + M ) V f ​ , so V f ​ = V 0 ​ /2 . For Q, 0 = ( M /3 ) v + ( 2 M /3 ) v h ​ , so v h ​ = − v /2 . For R, the COM of the man-boat system remains stationary. Thus, m x man ​ + M x b o a t ​ = 0 , leading to boat displacement Δ x b o a t ​ = − m L / ( M + m ) . For S, by conservation of momentum, 0 = m 1 ​ v 1 ​ + m 2 ​ v 2 ​ , so ∣ v 2 ​ ∣ = m 1 ​ v 1 ​ / m 2 ​ .

Physics - Center of Mass Question with Solution | TestHub

Options:

Doubts & Discussion