An Atwood machine consists of two blocks of masses M₁ and M₂ ( M₁ > M₂ ) connected by a light inextensible string passing over a smooth pulley. The system is released from rest and the heavier mass M₁ moves downwards with an acceleration a . If a small mass m is removed from M₁ and attached to M₂ , the system moves with a constant velocity. If instead, the same mass m is removed from M₂ and attached to M₁ , the downw

Step-by-step solution

Let the total mass of the system be M = M₁ + M₂ . The initial acceleration of the system is given by: a = M₁ - M₂ M₁ + M₂ g When mass m is transferred from M₁ to M₂ , the new masses are (M₁ - m) and (M₂ + m) . The system moves with constant velocity, which means the net force is zero (acceleration is zero). (M₁ - m)g = (M₂ + m)g M₁ - M₂ = 2m Substituting this into the initial acceleration equation: a = 2m M g When mass m is instead transferred from M₂ to M₁ , the new masses become (M₁ + m) and (M₂ - m) . The new ac