The acceleration due to gravity g and mean density of earth `rho` are related by which of the following relations ?
(G = gravitational constant and R = radius of earth)

Options

A. `rho=(4pigR^(2))/(3G)`
B. `rho=(4pigR^(3))/(3G)`
C. `rho=(3g)/(4pi GR)`
D. `rho=(3g)/(4pi GR^(3))`

Answer

C

Explanation

`g=(GM)/(R^(2))=(G((4)/(3)piR^(3))rho)/(R^(2)):. rho=(g)/(G.4pi(R)/(3))=(3g)/(4piGR)`