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Question

The masses of two planets are in the ratio 1:2. Their radii are in the ratio 1:2. The acceleration due to gravity on the planets are in the ratio:


A
1:2
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B
2:1
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C
3:5
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D
5:3
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Solution

The correct option is C 2:1
Let the mass of the first planet be M1
Let the radius of the first planet be R1
Let the mass of the second planet be M2
Let the radius of the second planet be R2

Acceleration due to gravity is given by:
g=GMR2

For the first planet, acceleration due to gravity is:
g1=GM1R21
For the second planet, acceleration due to gravity is:
g2=GM2R22

Taking the ratio,
g1g2=GM1/R21GM2/R22
g1g2=M1M2×R22R21

It's given that M2=2M1 and R2=2R1.
On substituting these in the expression, we get:
g1g2=12×2212
g1g2=21

Physics

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