A hanging block of mass m ' prevents the smaller block of mass m from slipping over a movable triangular block of mass M . All the surfaces are frictionless and the strings and the pulleys are light. Value of mass m ' in terms of m , M and θ is

Step-by-step solution

Pulling force is m ' g , while mass in motion is m + M + m ' . So acceleration of the system will be given by ​ a = m ' g m + M + m ' ....(i) Mass m will not slide over M if a cosθ = g sinθ ....(ii) From equation (i) in (ii), we get m ′ g cos θ m + M + m ′ = g sin θ or m ′ = m + M cot θ - 1