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Q.

A man stretches a horizontal spring of spring constant k attached to the wall of a railway carriage with uniform velocity‘v’ relative to carriage as shown in figure. Carriage is moving in same direction as stretching with uniform speed ‘u’. In ground's frame of reference

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a

Work done by man on spring in time t is 12kvv−u t2

b

Work done by man on spring in time t is 12kvv+u t2

c

Work done by trolley on spring in time t is −12kuv−u t2

d

Work done by trolley on spring in time t is −12kuv t2

answer is B.

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Detailed Solution

At time t elongation in spring = vtSpring force = kvt∴ work done by the man on spring =∫0t (kvt)(u+v)dt=12kv(u+v)t2∴ work done by trolley on spring =∫0t (kvt)(udt)(−1)=−12kuvt2

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