A small ball is placed at the top of a smooth hemispherical wedge of radius R. If the wedge is accelerated with an acceleration a, find the velocity of the ball relative to wedge as a function of `theta`.

Explanation

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

By the work energy theorem,

`W_(t otal)=triangleK`
`W_(gr)+W_(pseudo)=triangleK`
`mgR(1-costheta)+ma_0Rsin(theta)=(1)/(2)mv^2-0`
`v=sqrt(2R{g(1-costheta)+a_0sintheta})`
[The work done by normal reaction N is zero because it is always perpendicular to displacement.]