A body is taken to a height of nR from the surface of the earth . The ratio of acceleration due to gravity on the surface to that at the altitude is

Options

A. `(n+1)^(-2)`
B. `(n+1)^(2)`
C. `(n+1)`
D. `(n+1)^(-3)`

Answer

B

Explanation

`g=(GM)/(R^(2))`
and `g'=(GM)/((R+h)^(2))=(GM)/((R+nR)^(2))`
`=(GM)/([R(1+n)]^(2))=(GM)/(R^(2)(n+1)^(2))`
`therefore (g)/(g')=(GM)/(R^(2))xx(R^(2)(n+1)^(2))/(GM)=(n+1)^(2)`