The escape velocity from the Earth's surface is $v$ . The escape velocity from the surface of another planet having a radius, four times that of Earth and same mass density is:

Option 1 - <math> <mi mathvariant="normal">v</mi> </math>

Option 2 - <math> <mn>2</mn> <mi mathvariant="normal">v</mi> </math>

Option 3 - <math> <mn>3</mn> <mi mathvariant="normal">v</mi> </math>

Option 4 - <math> <mn>4</mn> <mi mathvariant="normal">v</mi> </math>

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Answered by

Alok Kumar Singh | Contributor-Level 10

5 months ago

Correct Option - 4

Detailed Solution:

$v_{e} = \sqrt[]{\frac{2 G M}{R}} = \sqrt[]{\frac{2 G}{R} * \frac{4}{3} π R^{3} ρ}$

$= \sqrt[]{\frac{8 π G ρ}{3} R^{2}}$

$\Rightarrow v_{e} \propto R$

$\Rightarrow \frac{v_{e}}{v} = \frac{4 R}{R} \Rightarrow v_{e} = 4 v$

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The escape velocity from the Earth's surface is v . The escape velocity from the surface of another planet having a radius, four times that of Earth and same mass density is:

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