A uniform solid sphere of mass 'm' and radius R is in equilibrium on an inclined plane by the action of the light spring of stiffness k, gravity and on it. If the angle of inclination of the plane is `60^(@)`, then find the time period of oscillation for small displancement.

Options

A. `2pi sqrt((m)/(10k))`
B. `2pi sqrt((7m)/(10k))`
C. `2pisqrt((7m)/(20k))`
D. `2pi sqrt((7m)/(40k))`

Answer

C

Explanation

`tau_(P) = k(2Rtheta) 2R`
`I_(Palpha) = -4kR^(2)theta`
`(7)/(5)mR^(2)alpha = -4kR^(2)theta`
`alpha = - ((20)/(7) (k)/(m)) theta`
`T = 2pi sqrt((7m)/(20k))`