One end of an unstretched vertical spring is attached to the ceiling and an object attached to the other end is slowly lowered to its equilibrium position. If S is the gain in spring energy and G is the loss in gravitational potential energy in the process, then

Options

A. S=G
B. S=2G
C. G=2S
D. None of these

Answer

C

Explanation

At equilibrium position ,`x=(mg)/(k)`
`U_("spring")=(1)/(2)kx^(2)=(1)/(2)((mg)/(k))x`
`=(mgx)/(2)=(1)/(2)`(loss in GPE)`implies`G=2S