Question

Three objects \(A, B\) and \(C\) are kept in a straight line on a smooth horizontal surface. These have masses \(m, 2m\) and \(3m\), respectively. The object \(A\) is given velocity \(v_0\) towards \(B\). The head-on elastic collision takes place between \(A\) and \(B\) and then \(B\) makes completely inelastic collision with \(C\). All motions occur on the same straight line. The final speed of \(C\) will be

Answer 1

Hint: “Head-on perfectly elastic and inelastic collision”

Formula used:

\(P_i=P_f\)

\(e=\dfrac{\text{Velocity of seperation}}{\text{velocity of approach}}\)

Solution:

The head-on elastic collision between \(A\) and \(B\)

\(mv_0=mv_1+2mv_2~~\ldots\ldots(i)\)

\(e=\dfrac{\text{Velocity of separation}}{\text{velocity of approach}}\)

\(v_1+v_0=v_2+0~~\ldots\ldots(ii)\)

Solving,

\(v_2=\dfrac{2v_0}{3}\)

Completely inelastic, the head-on collision between \(B\) and \(C\)

\(2m\times \dfrac{2v_0}{3}=(2m+3m)v\)

\(\Rightarrow v=\dfrac{4v_0}{15}\)

Final speed of \(C\)

\(v=\dfrac{4v_0}{15}\)

Final Answer: (d).