Imagine a new planet having the same density as that of earth but it is 3 times bigger than the earth in…
Imagine a new planet having the same density as that of earth but it is 3 times bigger than the earth in size. If the acceleration due to gravity on the surface of earth is $g$ and that on the surface of the new planet is $\mathrm{g}^{\prime}$ then:
$g^{\prime}=\frac{g}{9}$
$g^{\prime}=27 g$
$g^{\prime}=9 g$
$g^{\prime}=3 g$
Solution
$\begin{aligned}
g=\frac{G M}{R^2} & =\frac{G \frac{4}{3} \pi R^3 \rho}{R^2} \\
& =\frac{4}{3} G \pi R \rho \\
g^{\prime} & =\frac{4}{3} G \pi(3 R) \rho \\
& =3 g
\end{aligned}$
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