The density of a planet is rhoThe orbital period of a satellite revolving around it with remaining close to its surface is ..........

The density of a planet is rhoThe orbital period of a satellite revolv

1.	The density of a planet is rhoThe orbital period of a satellite revolving around it with remaining close to its surface is ..........
Answer» `((3pi)/(Grho))^(3/2)` `((3pi)/(Grho))^(1/2)` `((3pi)/(2Grho))^(3/2)` `((3pi)/(2Grho))^(1/2)` Solution :`implies` For planetary motion centripetal force = Gravitational force between planet and satellite `(mv^2)/R = (GMm)/(R^2)` `:.v = ((GM)/R)^(1/2)` `"Rw" = ((GM)/R)^(1/2)"" [ :. v = "rw"]` but , M = VOLUME `v xx` density `rho` `=4/3 piR^3 rho` `:. Rw=((G xx4/3piR^3rho)/R)1/2` `:. w = (4/3 PI Grho)^(1/2)` `:. T = (2pi)/w=(2pi)/((4/3piGrho)^(1/2))` `:. T = ((3pi)/(Grho))^(1/2)`