Two planets of radii r1 and r2 are made from the same material- The ratio of the acceleration due to gravity g 1- g 2 at the surface of the two planets isA- r 1 - r 2B- r 1 - r 22C- r 2 - r 12D- r 2 - r 1

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Universal Law of Gravitation

Two planets o...

Question

Two planets of radii $r_{1}$ and $r_{2}$ are made from the same material. The ratio of the acceleration due to gravity $\frac{g_{1}}{g_{2}}$ at the surface of the two planets is

r₁/r₂

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( r₁/r₂)²

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r₂/r₁

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(r₂/r₁)²

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Solution

The correct option is A
r₁/r₂

Since they are made of the same material, therefore, the density of both the planets would be same.

Mass of the planet = volume x density (volume = $\frac{4}{3}$ $π$ $r^{3}$ )

$g_{1}$ = $\frac{G \times \frac{4}{3} π {r_{1}}^{3}}{{r_{1}}^{2}}$ and $g_{2}$ = $\frac{G \times \frac{4}{3} π {r_{2}}^{3}}{{r_{2}}^{2}}$

On comparing both the ratio, we get, $\frac{r_{1}}{r_{2}}$

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