Physics - Gravitation Question with Solution | TestHub

Let $v$ be the orbital velocity of the satellite which is given as $v=\sqrt{\frac{GM}{r}}$

Here $M$ be the mass of the earth, $m$ be the mass of satellite and $r$ is the orbit radius.

Kinetic energy, $K=\frac{1}{2}m{v}^2=\frac{1}{2}m{\left(\sqrt{\frac{GM}{r}}\right)}^2=\frac{GMm}{2r}\propto \frac{m}{r}$

Ratio, $\frac{K_{\mathrm{A}}}{K_{\mathrm{B}}}=\frac{m_{\mathrm{A}}}{m_{\mathrm{B}}}\times \frac{r_{\mathrm{B}}}{r_{\mathrm{A}}}=\frac{m}{2m}\times \frac{2R}{R}=1$