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))`
D. `(R^(2))/((R+h)^(2))x`

Answer

D

Explanation

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