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 are in the ratio:

2:1

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3:5

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5:3

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1:2

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Solution

The correct option is A 2:1
Let the mass of the first planet be $M_{1}$
Let the radius of the first planet be $R_{1}$
Let the mass of the second planet be $M_{2}$
Let the radius of the second planet be $R_{2}$

Acceleration due to gravity is given by:
$g = \frac{G M}{R^{2}}$

For the first planet, acceleration due to gravity is:
$g_{1} = \frac{G M_{1}}{R_{1}^{2}}$
For the second planet, acceleration due to gravity is:
$g_{2} = \frac{G M_{2}}{R_{2}^{2}}$

Taking the ratio,
$\frac{g_{1}}{g_{2}} = \frac{G M_{1} / R_{1}^{2}}{G M_{2} / R_{2}^{2}}$
$\frac{g_{1}}{g_{2}} = \frac{M_{1}}{M_{2}} \times \frac{R_{2}^{2}}{R_{1}^{2}}$

It's given that $M_{2} = 2 M_{1}$ and $R_{2} = 2 R_{1}$ .
On substituting these in the expression, we get:
$\frac{g_{1}}{g_{2}} = \frac{1}{2} \times \frac{2^{2}}{1^{2}}$
$\frac{g_{1}}{g_{2}} = \frac{2}{1}$

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