Two massless wires A and B of the same material are joined in series and suspended from a rigid support. A block of mass M is attached to the free end of wire B. Wire A has length 3L and radius r , while wire B has length L and radius 2r . The ratio of the elastic potential energy stored in wire A to that stored in wire B is _____.

Step-by-step solution

For massless wires connected in series, the tension (force F ) is uniform and equal to the weight of the block Mg throughout both wires. The elastic potential energy stored in a wire is given by U = 1 2 F L . Since the force F is the same for both wires, the energy stored is directly proportional to the elongation, U L . The elongation of a wire is L = FL AY = FL r^2 Y . For wire A: L_A = F (3L) r^2 Y = 3 FL r^2 Y For wire B: L_B = F (L) (2r)^2 Y = 1 4 FL r^2 Y The ratio of the elastic potential energy stored in wi