Question

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 center. Their time periods are in the ratio of:

• A. $1:4\sqrt{2}$
• B. 1:8
• C. 1:32
• D. $1:2\sqrt{2}$

Answer 1

The correct option is D $1:2\sqrt{2}$

Mass of satellite does not affect time period

$\frac{T_A}{T_B}={\left(\frac{r_1}{r_1}\right)}^{3/2}={\left(\frac{r}{2r}\right)}^{3/2}={\left(\frac{1}{8}\right)}^{1/2}=\frac{1}{2\sqrt{2}}\therefore T_A=T_B=1:2\sqrt{2}$