Question

A planet of mass $4$ times that of the earth spins about itself and completes one rotation is $96$ hours. The radius of a stationary satellite about this planet in comparisons to the radius of the geostationary orbit around the earth is

• A. $4$ times
• B. $\left(\frac{1}{4}\right)$ times
• C. $2$ times
• D. $\left(\frac{1}{2}\right)$ times

Answer 1

Answer: (A)

$T=\frac{2\pi r^{\frac{3}{2}}}{\sqrt{GM}}$
$$\begin{gathered} \therefore Forearth,24=\frac{2\pi r^{\frac{3}{2}}}{\sqrt{GM}}..........(1) \\ Forplanet,96=\frac{2\pi r_1^{\frac{3}{2}}}{\sqrt{G\times 4M}}..........(2) \\ divide(2)\text{ by }(1) \\ \frac{96}{24}=\frac{1}{2}(\frac{r_1}{r}{)}^{\frac{3}{2}} \end{gathered}$$
$8={\left(\frac{r_1}{r}\right)}^{\frac{3}{2}}\Rightarrow \frac{r_1}{r}=4$
$r_1=4r$