Two identical blocks \(A\) and \(B\) each of mass \(m\) resting on the smooth horizontal floor are connected by a light spring of natural length \(L\) and spring constant \(K\). A third block \(C\) of mass \(m\) moving with a speed \(v\) along the line joining \(A\) and \(B\) collides with \(A\).The maximum compression in the spring is

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(A) \(v\sqrt{\frac{ M }{2 K }}\)

Step-by-step Solution

Detailed explanation

\(C\) comes to rest

\(V_{c m}\) of \(A \& B=\frac{v}{2}\)

\(\Rightarrow \frac{1}{2}\) is \(v _{ ret }^{2}=\frac{1}{2} kx ^{2}\)

\(x=\sqrt{\frac{\mu \times v^{2}}{k}}=\sqrt{\frac{m}{2 k}} v\)

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