Q.

Acceleration due to gravity on moon is 1/6 of the acceleration due to gravity on earth. If the ratio of densities of earth ρe and moon ρm is ρeρm=53 then radius of moon Rm in terms of Re will be

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a

518Re

b

16Re

c

318Re

d

123Re

answer is A.

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Detailed Solution

g=43πGρR ⇒ g∝ρR ⇒ gegm=ρeρm×ReRm⇒ 61=53×ReRm⇒Rm=518Re
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Acceleration due to gravity on moon is 1/6 of the acceleration due to gravity on earth. If the ratio of densities of earth ρe and moon ρm is ρeρm=53 then radius of moon Rm in terms of Re will be