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Q.

The radii of two planets ‘A’ and ‘B’ are ‘R’ and ‘4R’ and their densities are ρ and ρ/3 respectively. The ratio of acceleration due to gravity at their surfaces (gA:gB) will be 

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a

1 : 16

b

3 : 16

c

4 : 3

d

3 : 4

answer is D.

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Detailed Solution

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g=43πGρR

gAgB=RARB×ρAρB=R4R×ρ(ρ3)=34

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The radii of two planets ‘A’ and ‘B’ are ‘R’ and ‘4R’ and their densities are ρ and ρ/3 respectively. The ratio of acceleration due to gravity at their surfaces (gA:gB) will be