Two masses A & B each of 5 kg are suspended by a light inextensible string passing over a smooth massless pulley such that mass A rest on smooth table & B is held at the position shown. Mass B is now gently lifted up to the pulley and allowed to fall from rest. Determine up to what height will A rise for the ensuing

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When mass B (5 kg) is lifted and released, it accelerates downward due to gravity, pulling mass A (5 kg) horizontally on the smooth table. Since the pulley is smooth and massless, the tension is equal on both sides. The acceleration of the system is given by . Mass A moves horizontally with this acceleration. When B hits the ground, A has a velocity . After that, A continues moving with constant velocity (no acceleration) until it rises to a height on the curved path. Using energy conservation, the kinetic energy of A converts to potential energy: . Solving, . From kinematics, , where m (initial height). Substituting , , so m.
Final answer: 0.5 m