A solid cylinder of mass 3 kg is rolling on a horizontal surface with velocity 4 ms^-1. It collides with horizontal springs of force constant 200 Nm^-1. The maximum compression produced in the spring will be

0.5 m

0.6 m

0.7 m

0.2 m

Solution

0.6 m

Loss space in space straight K. straight E space equals space Gain space in space spring space energy 1 half mv squared open square brackets 1 plus straight K squared over straight R squared close square brackets space equals space 1 half kx subscript max superscript 2 where space straight k space is space the space force space constant. Given comma space straight v space equals space 4 space straight m divided by straight s comma space straight m equals space 3 space kg comma space straight k space equals space 200 space straight N divided by straight m For space solid space cylinder comma space straight K squared over straight R squared space equals 1 half therefore space 1 half space straight x space 3 space straight x space left parenthesis 4 right parenthesis squared open square brackets 1 plus 1 half close square brackets space equals space 1 half space straight x space 200 space straight x space space straight x subscript max superscript 2 The space maximum space compression space in space the space sspring straight x subscript max space equals space 0.6 space straight m

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