Q: A block of mass m is attached to one end of a mass less spring of spring constant *k*. The other end of spring of fixed to a wall. The block can move on a horizontal rough surface. The coefficient of friction between the block and the surface is μ . Then the compression of the spring for which maximum extension of the spring becomes half of maximum compression is

(a) (2mg μ )/k

(b) (mg μ)/k

(c) (4 mg μ)/k

(d) None of these

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Ans: (c)

Sol: Work done against friction = U

_{i}– U_{f}$\large \mu m g (x+ x/2) = \frac{1}{2}K x^2 – \frac{1}{2}K(x/2)^2 $

$\large 3 \mu m g x/2 = \frac{3 K x^2}{8}$

$\large x = \frac{4\mu m g}{K}$