A block M of mass 40 ~kg rests on a smooth horizontal surface. A block m₁ of mass 10 ~kg is placed on top of M and is connected by a weightless, inextensible string passing over a smooth, light pulley fixed at the right edge of M , to a hanging block m₂ of mass 10 ~kg . The block m₂ is in contact with the vertical right face of M . All surfaces are frictionless. A horizontal force F = 380 ~N is applied to M towards t

Step-by-step solution

Let a be the acceleration of block M to the right, and a_r be the downward acceleration of m₂ relative to M . For block m₂ in the vertical direction: m₂ g - T = m₂ a_r 100 - T = 10 a_r ... (i) For block m₁ in the horizontal direction (in the frame of M ): The pseudo force is m₁ a to the left. T - m₁ a = m₁ a_r T - 10 a = 10 a_r ... (ii) Adding (i) and (ii): 100 - 10 a = 20 a_r a = 10 - 2 a_r ... (iii) Considering the horizontal motion of the entire system, the external force F accelerates M and m₂ at a , and m₁ at