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A block of mass m is projected with velocity v as shown. The ground is smooth but there is friction between A and B. If collision is elastic, then choose the correct statement(s) (Assume that A does not fall of B) :-

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The final common velocity of A and B is $\frac{2 v}{9}$

The final common velocity of A and B is $\frac{4 v}{9}$

Total energy dissipated in friction is $\frac{2 m v^{2}}{9}$

Total energy dissipated in friction is $\frac{4 m v^{2}}{27}$

answer is B, D.

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Detailed Solution

After collision

After some time

$\begin{array}{l} v_{c o m m o n} = \frac{2 m (\frac{2 v}{3})}{3 m} \\ \Rightarrow v_{c o m m o n} = \frac{4 v}{9} \\ W_{f} = K_{f} - K_{i} = \frac{4}{27} m v^{2} \end{array}$

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