Question

A satellite of mass $m$ is moving around earth in a orbit of radius $r$. If another satellite has mass $2m$ and orbit's radius $2r$ then ratio of their time periods

• A. $2\sqrt{2}$
• B. $\frac{1}{2}$
• C. $\frac{1}{\sqrt{2}}$
• D. $\frac{1}{2\sqrt{2}}$

Answer 1

Answer: (A)

$2\sqrt{2}$

Time period of satellite depends only on radius of orbit and mass of the planet.

Using Kepler's law, $T^2\propto R^3$

Thus, $\frac{T_2^2}{T_1^2}=\frac{(2r{)}^3}{r^3}$

$⟹\frac{T_2}{T_1}=2\sqrt{2}$