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In the arrangement as shown, blocks $A$ and $B$ of the masses as shown move in the direction with velocities as indicated on a smooth surface. The spring constant is $300 N / m$ . Find the maximum compression in the spring (approx.) :

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$17 c m$

$22 c m$

$32 c m$

$38 c m$

answer is C.

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Detailed Solution

$\frac{1}{2} μ {v_{r}}^{2} = \frac{1}{2} k {x_{m}}^{2} \frac{1}{2} \times \frac{5}{6} \times 6^{2} = \frac{1}{2} \times 300 \times {x_{m}}^{2} x_{m} = \frac{1}{\sqrt{10}} m$

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