If `rho` is the mean density of the earth and R is its radius, then the critical speed of a satellite revolving very close to the surface of earth is :

Options

A. `2R sqrt((G pi rho)/(3))`
B. `2R sqrt((3G)/(pi rho))`
C. `2R sqrt((pi rho)/(3G))`
D. `2R sqrt((3)/(G pi rho))`

Answer

A

Explanation

`v_(c )=sqrt((GM)/(R ))=sqrt((G4 pi R^(3)rho)/(3R))=2R sqrt((G pi rho)/(3R))= 2R sqrt((G pi rho)/(3))`