A small block oscillates back and forth on a smooth concave surface of radius R. Find the time period of small oscillation.

Explanation

Restoring torque `tau=-mgRsintheta`
`I=mR^2`
`tau=-mgRtheta` (since `sin theta=theta`)
`Ialpha=-mgRtheta`
`alpha=-(mgR)/(I*)theta=-omega^2theta`
`T=2pisqrt((I)/(mgR))=2pisqrt((mR^2)/(mgR))`
`T=2pisqrt(R/g)`