Body of mass M is much heavier than the other body of mass m The heavier body with speed v collides with the lighter body which was at rest initially elastically. The speed of lighter body after collision is [AIIMS 2018]

detailed solution

Correct option is A

From law of conservation of momentum,               Mv + m × 0 = Mv1 + mv2⇒          M(v-v1) =mv2                                                     …(i)Again, from the conservation of kinetic energy (as collision is of elastic nature),        12Mv2+12m×0=12Mv12+12mv22⇒            Mv2-v12=mv22                                                  …(ii)On solving Eqs. (i) and (ii), we get             Mv-v1Mv+v1v-v1=mv2mv22                                    v2=v+v1Now, solving Eqs. (i) and (iiil, we get                            v1=(M-m)v(M+m)and                      v2 = 2Mv(M + m)As,                       M >>mSo,                          v1=v and v2=2vHence, velocity of lighter body (m) is 2v.