A uniform circular disc of mass 'm' and radius 'R' is placed on a rough horizontal surface and connected to the two ideal non-deformed spring of stiffness k and `2k` at the centre 'C' and point 'A' as shown . The centre of the disc is slighty displaced horizontally from equilibrium positon and then released, then the time period of small oscillation of the disc is (there is no slipping between the disc and the surface).

Options

A. `2pisqrt((5m)/(7k))`
B. `2pisqrt((3m)/(7k))`
C. `2pisqrt((5m)/(11k))`
D. `2pisqrt((3m)/(11k))`

Answer

D

Explanation

`(3mR^(2))/(2) (d^(2) theta)/(dt^(2)) = -kR^(2)theta - 3k Rtheta ((3R)/(2))`
`(3mR^(2))/(2) (d^(2)theta)/(dt^(2)) = - (11kR^(2)theta)/(2)`
`(d^(2)theta)/(dt^(2))= -((11K)/(3m)) theta`
`:.` Time Period, `T = 2pi sqrt((3m)/(11k))`