question_answer

A body of mass m moving with velocity u collides with a stationary body of mass 2m. The speed of the system after collision, is:

A)  \[2u\]                                  

B)  \[\frac{u}{3}\]

C)  \[2u\]                                  

D)  \[\frac{u}{4}\]

Correct Answer: B

Solution :

Key Idea: Momentum is conserved before and after Collision. From the principle of conservation of momentum, if no external force acts upon a system of two (or more) bodies then the total Momentum of the system remains constant. \[{{m}_{1}}{{u}_{1}}+{{m}_{2}}{{u}_{2}}={{m}_{1}}{{v}_{1}}+{{m}_{2}}{{v}_{2}}\] Given, \[{{m}_{1}}=m,\,\,{{u}_{1}}=u,\,\,{{m}_{2}}=2m,\,\,{{u}_{2}}=0\] (Stationary) \[\therefore \]  \[mu+2m\times 0=mv+2mv\] \[\Rightarrow \]                               \[v=\frac{u}{3}\] Hence, speed of system after the collision is \[\frac{u}{3}\].