A disc of mass `M` is attached to a horizontal massless spring of force constant `K` so that it can roll with out slipping along a horizontal surface. If the disc is pulled a little towards right and then released, its centre of mass executes `SHM` with a period of

Options

A. `2 pi sqrt((M)/(K))`
B. `2 pi sqrt((3M)/(K))`
C. `2 pi sqrt((M)/(2K))`
D. `2 pi sqrt((3M)/(2K))`

Answer

D

Explanation

`kx - f = ma " "f.R = I alpha rArr f = (Ia)/(R^(2)) (a = R alpha)`
`a = ((k)/(m + (I)/(R^(2))))x`
`T = 2pi sqrt((m)/(k) (1 + beta)), beta = (I)/(mR^(2))`