Thank you for reporting, we will resolve it shortly
Q.
Assuming density $d$ of a planet to be uniform, we can say that the time period of its artificial satellite is proportional to
Gravitation
Solution:
The time period of an artificial satellite revolving very close to the planet's surface is
$T=2 \pi \sqrt{\frac{R^{3}}{G M}}$
where $M$ is the mass of the planet and $R$ its radius.
Assuming the planet to be of uniform density $d$, so its mass is
$M=\frac{4}{3} \pi R^{3} d$
$\left(\right.$ as density $\left.=\frac{\text { mass }}{\text { volume }}\right)$
$\therefore d T=2 \pi \sqrt{\frac{R^{3}}{G\left(\frac{4}{3} \pi R^{3} d\right)}}$
$=\sqrt{\frac{3 \pi}{G d}}$ or $T \propto \frac{1}{\sqrt{d}}$