Two satellites 'A' and 'B' of same mass are revolving round the earth at height '2R' and '3R' respectively…

Two satellites 'A' and 'B' of same mass are revolving round the earth at height '2R' and '3R' respectively above the surface of the earth. The ratio of kinetic energies of A to B will be
  1. $3: 2$
  2. $3: 4$
  3. $2: 3$
  4. $4: 3$

Solution

$\begin{aligned} \text { K.E. } &=\frac{1}{2} \frac{\mathrm{GMm}}{\mathrm{r}} \\ \therefore \frac{\mathrm{K}_{1}}{\mathrm{~K}_{2}} &=\frac{\mathrm{r}_{2}}{\mathrm{r}_{1}} \\ &=\frac{3 \mathrm{R}+\mathrm{R}}{3 \mathrm{R}+\mathrm{R}}=\frac{4}{3} \end{aligned}$

Asked in: MHT CET 2020 (19 Oct Shift 1)

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