The average density and time period of a planet are rho and T. A satellite is revolving just above the surface of planet. If the universal gravitational constant is G, then T^(2) is equal to

The average density and time period of a planet are rho and T. A satel

1.	The average density and time period of a planet are rho and T. A satellite is revolving just above the surface of planet. If the universal gravitational constant is G, then T^(2) is equal to
Answer» `(3pi)/(G RHO)` `(4pi G)/(rho^(2))` `(4pi^(2)G)/(pi rho)` `(1)/(rho G pi)` Solution :As `v_(0) = sqrt((GM)/(R ))` `T = (2PI R)/(v_(0)) = (2pi R)/(sqrt((GM)/(R )))` `= 2pi sqrt((R^(3))/(GM)) = 2pi sqrt((R^(3))/(G.(4)/(3)pi R^(3) rho))` `T^(2) = 4pi^(2)(3)/(G xx 4 pi rho)` `T^(2) = (3pi)/(G rho)`