Two identical blocks, each of mass m , are connected in series by two elastic wires A and B and placed on a smooth horizontal table. Wire A connects the center of rotation to the first block, and wire B connects the first block to the second block. The system is rotated uniformly about the center with an angular velocity . The unstretched length of wire A is L and that of wire B is 2L . Both wires have the same cross

Step-by-step solution

Let the center of rotation be the origin. The first block is at a distance L from the center, and the second block is at a distance L + 2L = 3L from the center. The tension in wire B provides the centripetal force for the outermost block: T_B = m ^2 (3L) = 3m ^2 L The tension in wire A must provide the centripetal force for the inner block plus balance the outward pull of wire B: T_A - T_B = m ^2 (L) T_A = T_B + m ^2 L = 3m ^2 L + m ^2 L = 4m ^2 L According to Hooke's law, the elongation is given by L = T L₀ AY . F