For a given density of planet the orbital period of a satellite near the surface of planet of radius R is proportional to

R^1/2

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R^3/2

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R-^1/2

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R⁰

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Solution

The correct option is D
R⁰

$T = \frac{2 π r^{\frac{3}{2}}}{\sqrt{G M}}$

For $r \approx R$

and $M = \frac{4}{3} π R^{3} ρ$ ( $ρ$ = density of planet)

We see that $T = \sqrt{\frac{3 π}{ρ G}}$

i.e., T is independent of R.

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For a given density of planet the orbital period of a satellite near the surface of planet of radius R is proportional to

The correct option is D R0 T=2πr32√GM For r≈R and M=43πR3ρ (ρ = density of planet) We see that T=√3πρG i.e., T is independent of R.

The correct option is D
R⁰

$T = \frac{2 π r^{\frac{3}{2}}}{\sqrt{G M}}$

For $r \approx R$

and $M = \frac{4}{3} π R^{3} ρ$ ( $ρ$ = density of planet)

We see that $T = \sqrt{\frac{3 π}{ρ G}}$

i.e., T is independent of R.