A small block of mass `m` moving on inside of the smooth hemisphere of radius `R`, describes a horizontal circle at a distance `R//2` below the centre of the sphere. Find the time period of revolution and force with which the block pushes against the hemisphere.

Explanation

`N cos theta=mg` ….`(i)`
`implies N=(mg)/(cos theta)=(mg)/(1//2)=2mg`
`N sin theta theta=momega^(2)r` …..`(ii)`
`N sin theta=m omega^(2)R sin theta`
`implies N=momega^(2)R sin theta`
`implies N=momega^(2)R`
`2 mg=momega^(2)R`
`implies omega^(2)=(2g)/(R )impliesomega=sqrt((2g)/(R ))`
Time period `T_(0)=(2pi)/(omega)=2pisqrt((R )/(2g))`