The radii of two planets A and B are R and 4 R and their densities are ρ and ρ 3 respectively. The ratio of acceleration due to gravity at their surfaces g A : g B will be

Acceleration due to gravity is written as g = G M r 2 = G × 4 3 × π × r 3 × ρ r 2 = 4 π G 3 ρ r Given: r A = R r B = 4 R ρ A = ρ ρ B = ρ 3 Hence, the ratio is g A g B = R × ρ 4 R × ρ 3 = 3 4 .

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The radii of two planets $A$ and $B$ are $R$ and $4 R$ and their densities are $ρ$ and $\frac{ρ}{3}$ respectively. The ratio of acceleration due to gravity at their surfaces $(g_{A} : g_{B})$ will be

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Solution:

Acceleration due to gravity is written as $g = \frac{G M}{r^{2}} = \frac{G \times \frac{4}{3} \times π \times r^{3} \times ρ}{r^{2}} = (\frac{4 π G}{3}) ρ r$

Given:

$r_{A} = R r_{B} = 4 R ρ_{A} = ρ ρ_{B} = \frac{ρ}{3}$

Hence, the ratio is

$\frac{g_{A}}{g_{B}} = \frac{R \times ρ}{4 R \times \frac{ρ}{3}} = \frac{3}{4}$ .

Stream:JEESubject:PhysicsTopic:GravitationSubtopic:Acceleration Due to Gravity

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