A setellite os revolving very close to a planet of density p. The period of revolution of satellite is

Options

A. `sqrt3pip/G`
B. `sqrt3pi/2pG`
C. `sqrt3pi/pG`
D. `sqrt3piG/p`

Answer

C

Explanation

The time taken to copmplete one revolution is
T = `(2pi^r)/(V_o ) = ((2pi)(R_p+h))/(((GM_p)/(R_p+h)))`
`T= sqrt(4pi^2 (r_p+h))^3/GM_p` `[ therefore GM_e= gR(2/p)]`
The mass of the planet is given by
`M_p= (volume)xx(Density ) = 4/3 piR _p^2p`
Rightarrow T=`sqrt3pi/pG`