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. (a) `S=G`
B. (b) `S=2G`
C. (c) `G=2S`
D. (d) None of the above

Answer

C

Explanation

At equilibrium position, `x=(mg)/(k)`
`U_(spri ng)=1/2kx^2=1/2k((mg)/(k))x`
`=(mgx)/(2)-1/2(loss i n GPE)impliesG=2S`