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Q.

Block ‘A’ is hanging from a vertical spring and is at rest. Block ‘B’ strikes the block ‘A’ with ‘v’ and sticks to it. Then the value of ‘v’ (in m/s) for which the spring just attains natural length is

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answer is 6.

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Detailed Solution

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Applying conservation of energy between initial and final states
$\frac{1}{2} 2 m {(\frac{v}{2})}^{2} + \frac{1}{2} k {(\frac{m g}{k})}^{2} = 2 m g (\frac{m g}{k})$
Solving we get $v = \sqrt{\frac{6 m g^{2}}{k}} = 6 m / \sec$

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Block ‘A’ is hanging from a vertical spring and is at rest. Block ‘B’ strikes the block ‘A’ with ‘v’ and sticks to it. Then the value of ‘v’ (in m/s) for which the spring just attains natural length is