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Question

Ve,Vp denotes the escape velocity from the earth and another planet having twice the density as the earth, Then

A
Ve=Vp
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B
Ve=Vp/2
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C
Ve=2Vp
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D
Ve=Vp/4
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Solution

The correct option is B Ve=Vp/2

Mass=density×volume

M=ρV

Escape velocity

ve=2GMR=2GρVR=ρ2GρVR

veαρ

G= Gravitational Constants

R = Mass of the planet

ρ =density of planet

V = volume of planet

VeVp=ρeρp=ρe2ρe

Ve=Vp2

Hence, the relation between escape velocity Ve=Vp2

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