Question

A satellite $A$ of mass $m$ is at a distance of r from the surface of the earth. Another satellite $B$ of mass $2m$ is at a distance of $2r$ from the earth's centre. Their time periods are in the ratio of

• A. $1 : 2$
• B. $1 : 16$
• C. $1 : 32$
• D. $1: 2 \sqrt 2 $

Answer 1

Answer: (D)

Time period does not depend on the mass.
As $T^{2} \propto r^{3}$.
$\frac{T_{A}}{T_{B}}=\frac{r^{3 / 2}}{2^{3 / 2} r^{3 / 2}}=1: 2 \sqrt{2}$