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

Options

A. 0.5 m
B. 0.6 m
C. 0.7 m
D. 0.2 m

Answer

B

Explanation

At maximum compression the solid cylinder will stop.
According to law of conservation of mechanical energy
Loss in kinetic energy = Gain in potential energy of spring of cylinder
`1/2 mv^2 + 1/2 I omega^2 = 1/2 k x^2`
`1/2 mv^2 + 1/2 kx^2 " or " x^2 = 3/2 (mv^2)/(k)`
Here, `m = 3 kg , v = 4 ms^(-1), k = 200 N m^(-1)`
Substituting the given values , we get
`x^2 = (3 xx 3 xx 4 xx 4)/(2 xx 200) " or " x = 0.6 m`.