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Q.

Acceleration due to gravity on moon is 1/6 of the acceleration due to gravity on earth. If the ratio of densities pf 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

718Re

d

123Re

answer is A.

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Detailed Solution

Acceleration due to gravityg=43πρGR ∴g∝ρRor gmge=ρmρe⋅RmRe As gmge=16 and ρeρm=53 given ∴RmRe=gmgeρeρm=16×53 ∴ 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 pf earth ρe and moon ρm is ρeρm=53 then radius of moon Rm in terms of Re will be