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.

Options

A. `(M + m+m')(m')/(m)g`
B. `(M + m+m')(m')/(m + M)g`
C. `(M + m+m')(m')/(m' + M)g`
D. `(M + m+m')(M)/(m' + M)g`

Answer

a

Explanation

FBD The force acting on the block m and m' to the surface in contact are given an `mA larr,T rarr mg darr and T uarr`force equation relative to `M` Since `a_(mM) = a_(1) = 0`
For `m - Ma + T = 0`
For`M : T - m'g =0`
FromEqs(i) and (ii) `A = (m')/(m)g`

b. Force equation on `M + m+ m'`
`sum F_(x) = ma_(x)`
`F = MA + mA + m'A = (M+m+m')A`
`= (M+m+m')(m')/(m)g`