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

Solution

## The correct option is C 2:1Let 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=21Physics

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