A uniform disc of mass m is attached to a spring of spring constant k as shown in figure and there is sufficient friction to prevent slipping of disc. Time period of small oscillations of disc is:

Options

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

Explanation

Let centre of disc is displaced by x from its equilibrium position (spring was in its natural length). Now calculate the torque about lowest point of disc.
`k.3/2R.(3x)/2=3/2 mR^(2)a/R`
`(3kx)/(2m) =a`
So, `T=2pisqrt((2m)/(3k))`