If the ratio of the masses of two planets is $8 : 3$ and the ratio of their diameters is $2 : 3$ , then what will be the ratio of their acceleration due to gravity?

\frac{1}{6}

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\frac{6}{1}

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\frac{2}{3}

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\frac{9}{1}

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Solution

The correct option is C $\frac{6}{1}$ .
We know that $g = \frac{G M}{R^{2}}$
Given that,
$R_{2} : R_{1} = \frac{3}{2} = 1.5$ and $M_{1} : M_{2} = 8 : 3$
So,
$\frac{g_{1}}{g_{2}} = \frac{{G M}_{1}}{R_{1}^{2}} \div \frac{{G M}_{2}}{R_{2}^{2}}$
$\Rightarrow \frac{g_{1}}{g_{2}} = \frac{M_{1}}{M_{2}} \times \frac{R_{2}^{2}}{R_{1}^{2}}$
$= \frac{8}{3} \times {⎛ ⎜ ⎜ ⎜ ⎝ \frac{\frac{3}{2}}{1} ⎞ ⎟ ⎟ ⎟ ⎠}^{2}$
$= \frac{8}{3} \times \frac{9}{4}$
$= 6 : 1$

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Similar questions

\begin{matrix} If the ratio of the masses of two planets is 8 : 3 and the ratio of their diameters is 2 : 3, then what will be the ratio of their acceleration due to gravity? \end{matrix}

The masses of two planets are in the ratio 1: 2 and their radii are in the ratio 1: 2. The acceleration due to gravity on the planets is in the ratio

P_{1}

P_{2}

2 : 1

3 : 1

1 : 4

1 : 3

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