Planet A has mass M and radius R. Planet B has half the mass and half the radius of planet A. If the escape velocities from the planets A and B are $V_{A} a n d V_{B}$ respectively, then $\frac{V_{A}}{V_{B}} = \frac{n}{4}$ . The value of n is

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answer is B.

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Detailed Solution

The escape velocity from any planet’s surface $v_{e} = \sqrt{\frac{2 G m}{R}}$

So, $\frac{V_{A}}{V_{B}} = \sqrt{\frac{M_{A}}{M_{B}} \times \frac{R_{B}}{R_{A}}} = \sqrt{\frac{M_{A}}{\frac{1}{2} M_{A}} \times \frac{\frac{R_{A}}{2}}{R_{A}}} = 1$

$\frac{V_{A}}{V_{B}} = 1 \Rightarrow n = 4 [∴ \frac{V_{A}}{V_{B}} = \frac{n}{4}]$

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