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Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
हिन्दीA uniform metal bar of length 70 cm and mass 4.0 kg is supported horizontally on two knife-edges placed 10 cm from each end. A load of mass \( M \) is suspended at a distance of 30 cm from one end such that the reaction at the nearer knife-edge is exactly double the reaction at the farther knife-edge. Taking \( g = 9.8\text{ m/s}^2 \), the value of \( M \) is:
Correct answer · Option 3
2.0 kg
Explanation
Distance between knife-edges \( K_1K_2 = 50\text{ cm} \). Center of gravity G is at 35 cm from end A (\( K_1G = 25\text{ cm} \)). Load \( M \) is at 30 cm from end A (\( K_1P = 20\text{ cm} \), \( PK_2 = 30\text{ cm} \)). Taking torque about \( K_1 \): \( R_2(50) = 4g(25) + Mg(20) \implies 50R_2 = 100g + 20Mg \). With \( R_1 + R_2 = (4+M)g \) and \( R_1 = 2R_2 \implies 3R_2 = (4+M)g \). Equating gives \( M = 2.0\text{ kg} \).
