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  4. Two identical satellites are moving around the earth in circular orbits at heights 3R and R respectively where R is the radius of the Earth. The ratio of their kinetic energies is

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Q. Two identical satellites are moving around the earth in circular orbits at heights $3R$ and $R$ respectively where $R$ is the radius of the Earth. The ratio of their kinetic energies is

NTA AbhyasNTA Abhyas 2022

Solution:

The kinetic energy of satellites in a circular orbit is given as
$E_{k}=\frac{G M m}{2 r}\Rightarrow \, \frac{E_{k_{1}}}{E_{k_{2}}}=\frac{r_{2}}{r_{1}}=\frac{R + R}{R + 3 R}=\frac{2 R}{4 R}=\frac{1}{2}$