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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 16

Given 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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