Two similar springs P and Q have spring constants K P and K Q , such that K P > K Q . They are stretched, first by the same amount (case a), then by the same force (case b). the work done by the springs W P and W Q are related as respectively, in case

Step-by-step solution

K P > K Q Case (a): Stretched by same amount W P = 1 2 K P x 2 W Q = 1 2 K Q x 2 ∵ a s x P = x Q = x ∴ W P > W Q Case (b): Stretched by same force, F = K P x P = K Q x Q x P = F K P ; x Q = F K Q W P = 1 2 K P x P 2 = 1 2 K P F 2 K P 2 = 1 2 F 2 K P W Q = 1 2 K Q x Q 2 = 1 2 K Q F 2 K Q 2 = 1 2 F 2 K Q ∴ W P < W Q