If the period of revolution of an artificial satellite just above the earth's surface is T and the density of earth is ρ , then ρ T 2 is Options: A . &nbspA universal constant whose value is 3πG B . &nbspA universal constant whose value is 3π2G C . &nbspProportional to radius of earth R D . &nbspProportional to square of the radius of earth R2 Here, G= universal gravitational constant

If the period of revolution of an artificial satellite just above the earth&apos

Question

If the period of revolution of an artificial satellite just above the earth's surface is T and the density of earth is

ρ

, then

ρ T^{2}

Options:

A . A universal constant whose value is 3πG

B . A universal constant whose value is 3π2G

C . Proportional to radius of earth R

D . Proportional to square of the radius of earth R2 Here, G= universal gravitational constant

Answer: Option A
:
A
Here, G = universal gravitation constant
Time period of a satellite above the earth's surface is :

T^{2} = \frac{4 π^{2} R^{3}}{G M} = \frac{3 π}{G ⎛ ⎜ ⎝ \frac{M}{\frac{4}{3} π R^{3}} ⎞ ⎟ ⎠} = \frac{3 π}{G ρ}

ρ T^{2} = \frac{3 π}{G}

= a universal constant.

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