TS EAMCET · Physics · Gravitation
The ratio of the radii of two planets is ' \(\mathrm{r}\) ' and the ratio of accelerations due to gravity on the planets is ' \(x\) '. Then the ratio of the escape velocities from the planets is
- A \(\mathrm{xr}\)
- B \(\sqrt{\frac{r}{x}}\)
- C \(\sqrt{r x}\)
- D \(\sqrt{\frac{x}{r}}\)
Answer & Solution
Correct Answer
(C) \(\sqrt{r x}\)
Step-by-step Solution
Detailed explanation
(c) Escape velocity is given by: \[ \mathrm{v}=\sqrt{2 \mathrm{gR}} \] Ratio of radii of two planets, \(\frac{R_1}{R_2}=r\) Ratio of acceleration due to gravity of two planets, \[ \frac{\mathrm{g}_1}{\mathrm{~g}_2}=\mathrm{x} \] Ratio of escape velocity,…
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