Two springs A and B`(k_A=2k_B)` are stretched by applying forces of equal magnitudes at the force ends. If the energy stored in A is E, that in B is

Options

A. (a)`E//2`
B. (b)`2E`
C. (c)`E`
D. (d)`E//4`

Answer

B

Explanation

Let `k_A = 2k_B = K implies F = k_A x_A = k_B x_B implies x_A = F/K & x_B = (2F)/(K)`
`U_A - 1/2 k_A xx x_A^2 = 1/2 K(F/K)^2 = F/(2K) = E" "," " U_(B) = 1/2 k_Bx_B^2 = 1/2 k_B x^B^2 = 1/2K/2 ((2F)/(K))^(2) = (F^2)/K = 2E`.