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√2

Answer 1

Answer: (D)

1:2√2

Answer 2

The mass of a satellite does not affect the time period
$\frac{T_{A}}{T_{B}}=\left(\frac{r_{1}}{r_{1}}\right)^{3 / 2}=\left(\frac{r}{2 r}\right)^{3 / 2}=\left(\frac{1}{8}\right)^{1 / 2}=\frac{1}{2 \sqrt{2}}$
$\therefore$ TA= TB = 1:2√2

Hence, the correct option is d) 1:2√2.