Two springs P and Q of force constants `k_p and k_Q` are stretched by applying forces of equal magnitude. If the energy stored in Q is E, then the energy stored in P is

Options

A. a)E
B. b)2E
C. c)`E/8`
D. d)`E/2`

Answer

D

Explanation

Given `: k_p=2k_Q`
By stretching spring energy given
`E=1/2 kx^2 [ because F=kx]`
or `E=1/2 F^2/K`
For spring P
`E_p=1/2 F^2/K_p`
For spring Q
`E_Q=1/2 F^2/k_Q`
`therefore E_p/E_Q=k_Q/k_p= 1/2`
or `E_p=E_Q/2=E/2`