Find the mass of the hanging block in which will prevent the smaller block of mass m from slipping over the triangular block of mass M. All the surfaces are frictionless and the strings and the pulleys are light

Explanation

Let the mass of hanging block be m' then as pulling force is m'g while mass in motion `(m+M+m')`
So, `a=(m'g)/((m+M+m'))` ....(i)
The mass m will not slide over M if
`acos theta = gsin theta` …(ii)
Substituting the value of 'a' from eqn (i) and (ii)
`(m' gcos theta)/((m+M+m'))=g sin theta or m'=[(m+M)/(cot theta -1)]`