A solid uniform cylinder of mass `M` attached to a massless spring of force constant k is placed on a horizontal surface in such a way that cylinder can roll without slipping. If system is released from the stretched position of the spring, then the period will be-

Options

A. `2pisqrt((M)/(k)`
B. `2pisqrt((3m)/(2k))`
C. `2pisqrt((M)/(2k))`
D. `2pisqrt((2M)/(3k))`

Answer

B

Explanation

Let small angular displacement of cylinder be `theta` then restoring torque
`Ialpha = -k(Rtheta) R` where `I = 3/2 MR^(2)`
`rArr (d^(2)theta)/(dt^(2)) + (kR^(2))/((3)/(2)MR^(2)) theta = 0 rArr (d^(2)theta)/(dt^(2)) + (2k)/(3M)theta = 0 rArr omega^(2) = (2k)/(3m)`