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Question

Escape velocity from earth is about 11kms1. Escape velocity from a planet having twice the radius and same mean density as the earth is.

A
22kms1
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B
15.5kms1
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C
5.5kms1
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D
11kms1
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Solution

The correct option is A 22kms1
Let, ve be the escape velocity, G be the universal gravitational constant, M be the mass of the planet, R be the radius of the earth and ρ be the density of the earth.
We know, ve=2 GmR
We know mass of the planet, m=volume×density=43πR3×ρ
Therefore, ve=83 πρGR2
veR if ρ = constant.
Given escape velocity from the earth is about 11 kms1
Since the planet is having double the radius in comparison to earth, therefore the escape velocity becomes twice i.e. 2×11=22kms1.

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