Find the acceleration of the blocks A and B in the three situations shown in figure.

Explanation

Free body diagram

The block m does not slip over M'
From ure i. `T-N sin theta = M'a` ………….i.
`From ure ii, N cos theta = Mg`…..ii.
` N sin theta = Mg ……….iii`
` From ure iii, Mg-T=Ma`.......iv.
From equations i. and iv
`Mg-N sin theta = (M'+M) a`

From equation (ii),
`Mg-Mg tan theta j= (M'+M)a`
and a= g tan theta
`Mg-Mg tan theta = (M'+M)g tan theta`
:. M= (M'+M)/(cot theta -1)`.