Q131 / 160 · TS EAMCET 2023 (12 May Shift 2) · Physics
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$\sqrt{\frac{r}{x}}$
- Correct answerC$\sqrt{r x}$
- D$\sqrt{\frac{x}{r}}$
Solution
(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, $\frac{v_1}{v_2}=\sqrt{\frac{2 g_1 R_1}{2 g_2 R_2}}=\sqrt{\text { X.r }}$ Hence option (c) is correct answer.
Hence, the correct answer is option: 'C'.