A solid cylinder of mass 3 ~kg is rolling on a horizontal surface with velocity 4 ~m / s . It collides with a horizontal spring whose one end is fixed to rigid support. The force constant of material of spring is 200 ~N / m . The maximum co

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A solid cylinder of mass 3 ~kg is rolling on a horizontal surface with velocity 4 ~m / s . It collides with a horizontal spring whose one end is fixed to rigid support. The force constant of material of spring is 200 ~N / m . The maximum compression produced in the spring will be (assume collision between cylinder & spring be elastic)

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Correct answer: D. 0.6 ~m

At maximum compression, the solid cylinder will stop. So loss in K.E. of cylinder = Gain in P.E. of spring aligned & 1 2 mv ^2+ 1 2 I ^2= 1 2 kx ^2 & 1 2 mv ^2+ 1 2 mR ^2 2 ( v R )^2= 1 2 kx ^2 & 3 4 mv ^2= 1 2 kx ^2 & 3 4 3 (4)^2= 1 2 200 x ^2 & 36 100 = x ^2 x =0.6 ~m aligned

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