Imagine a new planet having the same density as that of earth but...

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:

Options

A $g^{\prime}=\frac{g}{9}$
B $g^{\prime}=27 g$
C $g^{\prime}=9 g$
D $g^{\prime}=3 g$

Correct answer

D. $g^{\prime}=3 g$

Step-by-step 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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