Two blocks \( A \) and \( B \) each of mass \( m \), are connected by a massless spring of natural length \( L \) and spring
\( \mathrm{P} \)
constant ' \( k \) '. The blocks are initially resting on a smooth horizontal floor with the spring at its natural
W
length, as shown in figure. A third identical block \( C \), also of mass \( m \), moves on the floor with a speed \( v \) along the line joining \( A \) and \( B \) and collides elastically with \( A \). Then
(1) The kinetic energy of the \( A-B \) system, at maximum compression of the spring is zero
(2) The kinetic energy of the \( A-B \) system, at maximum compression of the spring is \( m v^{2} / 4 \)
(3) The maximum compression of the spring is \( v \sqrt{(m / k)} \)
(4) The maximum compression of the spring is
\[
v \sqrt{\frac{m}{2 k}}
\]
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