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A solid cylinder of mass 3 kg is rolling without slipping on a horizontal smooth surface with velocity 4 ${ms}^{- 1}$ . It collides with a smooth horizontal spring of force constant 200 ${Nm}^{- 1}$ . The maximum compression produced in the spring will be

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0.49 m

0.2 m

0.5 m

0.7 m

answer is C.

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Detailed Solution

KE OF TRANSLATION IS EQUAL TO THE WORKDONE IN COMPRESSING THE SPRING.AFTER THE IMPACT ROTATIONAL MOTION OF THE CYLINDER DOES NOT STOP.

$\frac{1}{2} m v^{2} = \frac{1}{2} k x^{2} \Rightarrow x = v \sqrt{\frac{m}{k}} \Rightarrow x = 4 \sqrt{\frac{3}{200}} m = 0.49 m$ ,

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