If `rho` is the density of the planet , the time period of nearby satellite is given by

Options

A. `sqrt((4pi)/(3G rho))`
B. `sqrt((4pi)/(G rho))`
C. `sqrt((3pi)/(G rho))`
D. `sqrt((pi)/(G rho))`

Answer

C

Explanation

Time period of nearby satellite
`T=2pi sqrt((r^(3))/(GM))`
`=2pi sqrt((R^(3))/(GM))`
`=(2 pi (R^(3))^(1//2))/([G*(4)/(3)piR^(3)rho]^(1//2))`
`=sqrt((3pi)/(G rho))`