A mass `m` extends a vertical helical spring of spring constant `k` by `xm` at the surface of the earth. Extension in spring by the same mass at height `h` meter above the surface of the earth is

Options

A. `(Gmm)/(k(R+h))`
B. `(GMm)/(kR^(2))`
C. `((R+h)^(2))/(R^(2)) x`
D. `(R^(2))/((R+h)^(2)) x`

Answer

D

Explanation

Let the extension at height h be x. then
`x=(GMm)/(kR^(2))` ( `:. F=kx` or `x=F/k`)
then `(x.)/x=(R^(2))/(k(R+h)^(2)), x.=(R^(2))/((R+h)^(2))x`