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

Question

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

Quantrex Academy · Accepted Answer

Correct answer: C. W _ P > W _ Q ; W _ Q > W _ P

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 (∵ as 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

Two similar springs P and Q have spring constants K _ P and K _ Q ,...

Options

Correct answer

Step-by-step solution

More from Work, Power and Energy