Assuming density d of a planet to be uniform, we can say that the time period of its artificial satellite is proportional to:

Options

A. d
B. `sqrt(d)`
C. `(1)/(sqrtd)`
D. `(1)/(d)`

Answer

C

Explanation

The time period of an artificial satellite revolving very close to the planet's surface is
`T=2pisqrt((R^3)/(GM))`
Where M is the mass of the planet and R its radius. Assuming the planet to be of uniform density d, so its mass is
`M=(4)/(3)piR^(3)d" "("As density"=("mass")/("volume"))`
`thereforeT=2pisqrt((R^3)/(G((4)/(3)piR^3d)))=sqrt((3pi)/(Gd))`
(or) `Tprop(1)/(sqrtd)`