Consider a planet whose density is same as that of the earth but whose radius is three times the radius ' \(R\) ' of the earth. The acceleration due to gravity ' \(\mathrm{g}_{\mathrm{n}}\) ' on the surface of planet is \(g_n=x\). \(g\) where \(g\) is acceleration due to gravity on surface, of earth. The value of ' \(\mathrm{x}\) ' is

\(\begin{array}{ll}
& \mathrm{As}, \mathrm{g}=\frac{\mathrm{GM}}{\mathrm{R}^2} \text { and } \mathrm{M}=\rho \mathrm{V} \\
\therefore \quad & \mathrm{g}=\frac{\mathrm{G} \rho \mathrm{V}}{\mathrm{R}^2}=\frac{\mathrm{G} \rho \frac{4}{3} \pi \mathrm{R}^3}{\mathrm{R}^2} \\
\therefore \quad & \mathrm{g} \propto \mathrm{R}
\end{array}\)
For the planet: Radius \(\mathrm{R}=3 \mathrm{R}\)
\(\begin{array}{ll}
\therefore \quad & \mathrm{g}_{\text {planet }}=\frac{\mathrm{G} \mathrm{V}_{\text {planet }}}{(3 \mathrm{R})^2} \\
& \text { where } \mathrm{V}_{\text {planet }}=\frac{4}{3} \pi(3 \mathrm{R})^3 \\
\therefore \quad & \mathrm{g}_{\text {planet }}=\frac{\mathrm{G} \rho \frac{4}{3} \pi(3 \mathrm{R})^3}{(3 \mathrm{R})^2} \\
\therefore \quad & \mathrm{g}_{\text {planet }} \propto 3 \mathrm{R}
\end{array}\)
\(\therefore \quad \frac{\mathrm{g}}{\mathrm{g}_{\text {planet }}}=\frac{\mathrm{R}}{3 \mathrm{R}} \quad\)....(since \(\rho\) is constant)
\(\begin{array}{ll}\therefore & \mathrm{g}_{\text {planet }}=3 \mathrm{~g} \\ \therefore & \mathrm{x}=3\end{array}\)