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Question

# Two planets of radii r1 and r2 ​are made from the same material. The ratio of the acceleration due to gravity g1g2​ at the surface of the two planets is:

A

r1r2

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B

(r1r2)2

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C

r2r1

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D

(r2r1)2

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Solution

## The correct option is A r1r2​ Since both the planets are made of the same material, the density of both the planets would be the same. We know, mass of the planet = volume × density Let, ρ be the density of the material. Volume = 43πr3, where 'r' is the radius of the planet. We know, F=mg=GMmr2 ⇒g=GMr2 =G43πr3ρr2 Let radius of first planet be r1 and acceleration due to gravity be g1 ⇒g1=G×43πr13ρr12=43πGr1ρ and for the second planet, let the radius be r2 and acceleration due to gravity be g2 ⇒ g2=G×43πr23ρr22=43πGr2ρ On dividing g1 by g2, we get, g1g2=r1r2

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