Question

# The acceleration due to gravity on the moon is only one sixth that of earth, If the earth moon are assumed to have same density. The ratio of the radii of moon and earth will be

A
16
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B
16(1/3)
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C
136
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D
16(2/3)
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Solution

## The correct option is A 16Given that, The acceleration due to gravity on the moon is only one sixth that of earth gm=gE6 Now, The acceleration due to gravity on moon gm=43πRmGρ....(I) We know that, The acceleration due to gravity on earth gE=GmR2 gE=G(43πR3ρ)R2 gE=43πGRρ.....(II) Now, from equation (II) and (I) The ratio of the acceleration due to gravity on earth and moon gmgE=RmRE gE6×gE=RmRE RmRE=16 Hence, the ratio of the radii of moon and earth will be 16

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