First slide

Gravitaional potential energy

Question

The ratio of the radii of the planets P₁ and P₂, is K₁. The ratio of the acceleration due to the gravity on them is K₂ The ratio of the escape velocities from them will be

Easy

A

K₁K₂
B

$\sqrt{k_{1} k_{2}}$
C

$\sqrt{(k_{1} / k_{2})}$
D

$\sqrt{(k_{2} / k_{1})}$

Solution

$v_{e} = \sqrt{2 gR}$
$\begin{array}{l} ∴ \frac{{(v_{e})}_{p_{1}}}{{(v_{e})}_{p_{2}}} = \frac{\sqrt{g_{1} R_{1}}}{\sqrt{g_{2} R_{2}}} \\ = \sqrt{\{(\frac{g_{1}}{g_{2}}) \times (\frac{R_{1}}{R_{2}})} = \sqrt{k_{1} k_{2}} \end{array}$

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