Two smooth blocks of masses m and m' connected by a light inextensible strings are moving on a smooth wedge of mass M. If a force F acts on the wedge the blocks do not slide relative to the wedge. Find the (a) acceleration of the wedge and (b) value of F.

Explanation

The force acting on the block m and m' parallel to the surface in contact are given as `mA larr, t rarr, m'g darr`, and `T uarr`.

Force equation relative to M: since `a_(mM)-a_(0)=0`
for `m:T=ma`...(i)
for `m':T=m'g` ...(ii)
From Eq,(i) and (ii) `A=(m')/(m) g`
(b) Force equation on system `'M+m+m'`
`Sigma F_(x)=ma_(x)`
`F=MA+mA+m'A`
`=(M+m+m')A`
`(M+m+m')(m')/(m)g`.