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 is in the ratio:

1:2

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2:1

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3:5

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5:3

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Solution

The correct option is B
2:1

The expression of 'g' on the Earth is, g = $\frac{G M}{R^{2}}$

Let $M_{1}$ and $M_{2}$ be the masses and $R_{1}$ and $R_{2}$ be the radii of the planets respectively.

So, the acceleration due to gravity on planet 1 and 2 are

$g_{1}$ = $\frac{G M_{1}}{{R_{1}}^{2}} - - - - (1)$ and $g_{2}$ = $\frac{G M_{2}}{{R_{2}}^{2}} - - - - (2)$ respectively.

It's given that $M_{2}$ = $2 M_{1}$ and $R_{2}$ = $2 R_{1}$
On substituting these in the equation (2), we will get:

$g_{2}$ = $\frac{G 2 M_{1}}{{(2 R_{1})}^{2}}$

$⟹ g_{2} = \frac{1}{2} \frac{G M_{1}}{{R_{1}}^{2}}$

$⟹ g_{2} = \frac{1}{2} g_{1}$

$\frac{g_{1}}{g_{2}}$ = 2:1

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