A block is placed at the top of a smooth hemisphere of radius `R`. Now the hemisphere is given a horizontal acceleration `a_0`. Find the velocity of the block relative to the hemisphere as a function of `theta` at it slides down.

Explanation

In the reference frame of hemisphere. Apply a pseudo force on m.

From the work-energy theorem,

`W_("total")=Delta K implies W_(gr)+W_(pseudo)=Delta K`
`mgR(1-cos theta)+ma_(0)R sin theta=(1)/(2)mv^(2)-0`
`v=sqrt(2R{g(1-costheta)+a_(0)sin theta))}`
The work done by normal reaction N is zero because it is always perpendicular to displacement.