MHT CET · Physics · Gravitation
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
- A \(3: 2\)
- B \(3: 4\)
- C \(2: 3\)
- D \(4: 3\)
Answer & Solution
Correct Answer
(D) \(4: 3\)
Step-by-step Solution
Detailed explanation
(B)
\(\begin{aligned}
\text { K.E. } &=\frac{1}{2} \frac{\mathrm{GMm}}{\mathrm{r}} \\
\therefore \frac{\mathrm{K}_{1}}{\mathrm{~K}_{2}} &=\frac{\mathrm{r}_{2}}{\mathrm{r}_{1}} \\
&=\frac{3 \mathrm{R}+\mathrm{R}}{3 \mathrm{R}+\mathrm{R}}=\frac{4}{3}
\end{aligned}\)
\(\begin{aligned}
\text { K.E. } &=\frac{1}{2} \frac{\mathrm{GMm}}{\mathrm{r}} \\
\therefore \frac{\mathrm{K}_{1}}{\mathrm{~K}_{2}} &=\frac{\mathrm{r}_{2}}{\mathrm{r}_{1}} \\
&=\frac{3 \mathrm{R}+\mathrm{R}}{3 \mathrm{R}+\mathrm{R}}=\frac{4}{3}
\end{aligned}\)
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