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Q.

The escape velocities of two planets A and B are in the ratio 1:2. If the ratio of their radii respectively is 1:3, then the ratio of acceleration due to gravity of planet A to the acceleration due to gravity of planet B will be:

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a

$\frac{3}{4}$

b

$\frac{2}{3}$

c

$\frac{4}{3}$

d

$\frac{3}{2}$

answer is A.

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Detailed Solution

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Escape velocity on a planet $V = \sqrt{2 gR}$
$\frac{V_{A}}{V_{B}} = \frac{1}{2} \frac{R_{A}}{R_{B}} = \frac{1}{3}$
$\begin{array}{l} \frac{V_{A}^{2}}{V_{B}^{2}} = \frac{2 g_{A} R_{A}}{2 g_{B} R_{B}} \Rightarrow \frac{1}{4} = \frac{g_{A} \times 1}{g_{B} \times 3} \\ \frac{g_{A}}{g_{B}} = \frac{3}{4} \end{array}$

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