Q: Two springs have force constants k_{A} and k_{B} = 2k_{A}. The four ends of the springs are stretched by the same force. Energy stored in spring A is E, then energy stored in spring B is

(a) E/2

(b) 2E

(c) E

(d) 4E

Ans: (a)

Sol: $\displaystyle U_A = \frac{1}{2}k_A x_A^2 $

$\displaystyle U_A = \frac{k_A^2 x_A^2}{2 k_A} = \frac{F^2}{2k_A} $

Similarly , $ \displaystyle U_B = \frac{F^2}{2k_B} $

$\displaystyle \frac{U_A}{U_B} = \frac{k_B}{k_A} = 2 $

$\displaystyle \frac{E}{U_B} = 2 $

$ \displaystyle U_B = \frac{E}{2} $