The spring is compressed by a distance ‘ $a$ ’ and released. The block again comes to rest when the spring is elongated by a distance ‘b’ from natural length. From the point of maximum compression to maximum elongation, Find

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Coefficient of friction $= \frac{k (a + b)}{2 m g}$

Coefficient of friction $= \frac{k (a - b)}{2 m g}$

Work done by the spring on the block $= \frac{1}{2} k (a^{2} - b^{2})$

Work done by the spring on the block $= \frac{1}{2} k {(a + b)}^{2}$

answer is B, C.

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Detailed Solution

Work done by spring on block
Question Image
$w_{s} = \frac{1}{2} k a^{2} - \frac{1}{2} k b^{2} = \frac{1}{2} k (a^{2} - b^{2})$
By work energy theorem,
$K_{i} + w = K_{f}$
$0 + \frac{1}{2} k a^{2} - μ m g (a + b) - \frac{1}{2} k b^{2} = 0$
$\begin{array}{l} μ m g (a + b) = \frac{1}{2} k (a^{2} - b^{2}) \\ μ = \frac{k (a - b)}{2 m g} \end{array}$