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Escape Speed

The ratio of ...

Question

The ratio of the radii of two planets $r_{1}$ and $r_{2}$ is $k$ . The ratio of acceleration due to gravity on them is $r$ . Then the ratio of the escape velocities from them, will be:

A

\sqrt{\frac{r}{k}}

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B

\sqrt{\frac{k}{r}}

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C

k r

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D

\sqrt{k s}

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Solution

The correct option is C $\sqrt{k s}$
Ratio of radii: $\frac{r_{1}}{r_{2}} = k$
Ratio of acceleration due to gravity: $\frac{g_{1}}{g_{2}} = r$
Ratio of escape velocity: $\frac{v_{1}}{v_{2}} = \sqrt{\frac{g_{1} r_{1}}{g_{2} r_{2}}} = \sqrt{k r}$

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