Two springs P and Q are stretched by applying forces of equal magnitudes at the four ends. If the spring constant of P is 2 times greater than that of Q and the energy stored in P is E, then the energy stored in Q is :

Options

A. E/4
B. E/2
C. E
D. 2E

Answer

D

Explanation

Let the spring constant of spring Q is k and that of P is 2k. The extensions produced by applying equal forces on them are `x_(P)` and `x_(Q)`, respectively. Since F = kx (numerically)
or `x=(F)/(k)` and `U=(1)/(2)kx^(2)`
or `U=(1)/(2)k((F)/(k))^(2)=(F^(2))/(2k)`
or `U prop (1)/(k)`
Thus, `(U_(Q))/(U_(P))=(k_(P))/(k_(Q))=(2k)/(k)=2`
or `U_(Q)=2U_(P)=2E`