All the surfaces shown in figure are assumed to be frictionless. The block of mass m slides on the prism which in turn slides backward on the horizontal surface. Find the acceleration of the smaller block with respect to the prism.

Explanation

Let the acceleration of the prism be `a_0` in the backward direction. Consider the motion of the smaller block fro the frame of the prism.
The force on the block are

i. N normal force,
mg downward (gravity)
`ma_0` forward (psuedo)`

The block slides down the plane. components of the forces parallel to the incline give
`ma_0costheta+mg sintheta=ma`
or, `a=a_0costheta+g sin theta` .........i
Components of teh force perpendicular to the incline give
`N +ma_0sintheta=mg costheta` .........ii
Non consider the motion of the prism from the lab frame. No pseudo force isneeded as the frame used is inertial. The forces are ure 16 b
i. Mg downward,
ii. N normal to the incline (by the block)
`N upward (by the horizontal surface).
Horizontal components give,
`N sintheta=Ma_0 or, N Ma_0/sintheta` ..............iii
Putting in ii.
`(Ma_0)/(sintheta)+ma_0 sintheta=costheta`
or, `a_0 = (mg sinthetacostheta)/(M+msin^2theta)`
From i. `a=(mg sintheta cos^2theta)/(M+msin^2theta)+g sintheta`
`=((M+m)g sintheta)/(M+m sin^2 theta)`