Consider two wires, A and B , composed of the same material. Wire A possesses a length l and diameter r , whereas wire B has a length 2l and diameter r/2 . When both wires are stretched by an identical force, the ratio of the elongation in A to the elongation in B is

Step-by-step solution

Young's modulus is given by Y = F L A L The elongation of a wire is L = F L A Y = 4 F L d^2 Y For wire A , length L_A = l and diameter d_A = r . The elongation is: L_A = 4 F l r^2 Y For wire B , length L_B = 2l and diameter d_B = r/2 . The elongation is: L_B = 4 F (2l) (r/2)^2 Y = 32 F l r^2 Y Taking the ratio of the elongations: L_A L_B = 4 F l r^2 Y 32 F l r^2 Y = 4 32 = 1 8