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

One end of ………….
At equilibrium position `x = (mg)/(x)`
`U_("spring") = (1)/(2)kx^(2)= (1)/(2)k ((mg)/(k))x = (mg x)/(2)`
`= (1)/(2)(loss in G.P.E.)`
`implies G = 2s`