If `R` is the radius of the earth and `g` the acceleration due to gravity on the earth's surface, the mean density of the earth is

Options

A. `(3g)/(4pi GR)`
B. `(4pi g)/(3GR)`
C. `(3pi GR)/(4g)`
D. `(4pi R)/(3gG)`

Answer

A

Explanation

`g=(GM)/(R^(2))=(G)/(R^(2))((4)/(3)pi R^(3)d)=(4pi GRd)/(3)`
`therefore d = (3g)/(4pi GR)`