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Question

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

A
4v
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B
v
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C
2v
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D
3v
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Solution

The correct option is A 4v
Escape velocity from the Earth's surface,

ve=2GMR=2G[ρ×(4πR3/3)]R

ve=8GρπR23

veR (For same density)

v1v2=R1R2vv2=R4R

v2=4v

Hence, option (A) is correct.

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