First slide

Gravitaional potential energy

Question

The ratio of escape velocity at earth (v_e) to the escape velocity at a planet (v_p ) whose radius and mean density are twice as that of earth is :

Moderate

A

1 :2
B

$1 : 2 \sqrt{2}$
C

1:4
D

$1 : \sqrt{2}$

Solution

Escape velocity = $= \sqrt{\frac{2 GM}{R}} = \sqrt{\frac{2 G}{R} (\frac{4}{3} {πR}^{3} ρ)} \propto R \sqrt{ρ}$
$∴ Ratio, \frac{v_{e}}{v_{p}} = 1 : 2 \sqrt{2}$

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