The ratio of escape velocity of a planet to the escape velocity of Earth will be: Given: Mass of the planet is 16 times the mass of Earth and radius of the planet is 4 times the radius of Earth. [2023]

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Solution

Q.
The ratio of escape velocity of a planet to the escape velocity of Earth will be:

Given: Mass of the planet is 16 times the mass of Earth and radius of the planet is 4 times the radius of Earth. [2023]

1 4 : 1

2 2 : 1

3 1 : $\sqrt{2}$

4 1 : 4

Ans.
(2)

$v_{escape} = \sqrt{\frac{2 G M}{R}}$

$∴$ $v_{escape} for planet = \sqrt{\frac{2 G (16 M_{E})}{4 R_{E}}} = 2 \sqrt{\frac{2 G M_{E}}{R_{E}}}$

$= 2 (v_{escape} for Earth)$

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