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Question

The escape velocity from the earth is 11kms-1. The escape velocity from a planet having twice the radius and same mean density as that of earth is


A

5.5kms-1

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B

11kms-1

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C

22kms-1

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D

None of these

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Solution

The correct option is C

22kms-1


Step 1: Given data

Escape Velocity ve=11kms-1

Step 2: Formula Used

The earth's escape velocity is given by ve=GMR1

Where, Escape Velocity =ve, G = universal gravitational, M = mass of the earth, and R = radius of the earth

The radius of the planet Rpis twice the radius of the earthRe

i.e.Rp=2Re

ρp=ρe, where ρp is the density of the planet and ρeisdensityofearth

Step 3: Calculation of the escape velocity,

v=2GMR=2G×43πR3ρR=83πGR2ρvρR2

Therefore,

vpve=ρe(2Re)2ρeRe2vp11=ρe(2Re)2ρeRe2=2vp=22km/s

Hence, option C is the correct answer.


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