Two blocks of masses $m_{1} = 2 k g$ and $m_{2} = 4 k g$ are moving in the same direction with speeds $v_{1} = 6 m / s$ and $v_{2} = 3 m / s$ , respectively on a frictionless surface as shown in figure. An ideal spring with spring constant $k = 30000 N / m$ is attached to the back side of $m_{2}$ . Then the maximum compression of the spring after collision will be

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$0.06 m$

$0.04 m$

$0.02 m$

None of these

answer is C.

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Detailed Solution

At the time of maximum compression, the speeds of blocks will be the same. Let that speed be v and maximum compression be $x$ .
Applying conservation of momentum,
$(m_{1} + m_{2}) v = m_{1} v_{1} + m_{2} v_{2} \Rightarrow v = 4 m / s$
Applying conservation of mechanical energy
$\frac{1}{2} k x^{2} + \frac{1}{2} (m_{1} + m_{2}) v^{2} = \frac{1}{2} m_{1} v_{1}^{2} + \frac{1}{2} m_{2} v_{2}^{2}$
Solving, we get $x = 0.02 m$