Question

If the period of revolution of a nearest satellite around a planet of radius R is T then its period of revolution around another planet, having radius 3R and same density will be :

• A. $T$
• B. $3T$
• C. $3\sqrt{3}T$
• D. $9T$

Answer 1

Answer: (A)

$T$

For a nearest satellite, the period of revolution is
$T=2\pi \sqrt{\frac{R^3}{GM}}=2\pi \sqrt{\frac{R^3}{G\frac{4}{3}\pi R^{3}p}}$
$T\propto \sqrt{\frac{1}{p}}$
i.e., the period of revolution depends upon the density of the planet. Here, the density of the planets is same, therefore time period will be same.