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")=1/2kx^(2)=1/2k((mg)/k).x=(mgx)/2`
`=1/2` (loss in G.P.E)
`impliesG=2S`