A planet of volume V and mass m has gravitational acceleration g on its surface. If it expands to 8 times its original volume, what will be the acceleration due to gravity

4

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2

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g / 4

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g / 8

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Solution

The correct option is D $g / 4$
$∵ \frac{4}{3} π r^{3} \times 8 = \frac{4}{3} π R^{3} \Rightarrow R = 2 r$
$g = \frac{G M}{r^{2}}, g^{'} = \frac{G M}{R^{2}}$
$\Rightarrow (\frac{g^{'}}{g}) = \frac{r^{2}}{R^{2}} ∴ g^{'} = \frac{g}{4}$ .

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A planet of volume V and mass m has gravitational acceleration g on its surface. If it expands to 8 times its original volume, what will be the acceleration due to gravity

The correct option is D g/4∵43πr3×8=43πR3⇒R=2rg=GMr2,g′=GMR2⇒(g′g)=r2R2∴g′=g4.

The correct option is D $g / 4$
$∵ \frac{4}{3} π r^{3} \times 8 = \frac{4}{3} π R^{3} \Rightarrow R = 2 r$
$g = \frac{G M}{r^{2}}, g^{'} = \frac{G M}{R^{2}}$
$\Rightarrow (\frac{g^{'}}{g}) = \frac{r^{2}}{R^{2}} ∴ g^{'} = \frac{g}{4}$ .