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A uniform solid sphere of mass 'm' and ...

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.

A

`2pi sqrt((m)/(10k))`

B

`2pi sqrt((7m)/(10k))`

C

`2pisqrt((7m)/(20k))`

D

`2pi sqrt((7m)/(40k))`

Text Solution

Verified by Experts

The correct Answer is:
C
`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))`
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