Physics - Gravitation Question with Solution | TestHub

The acceleration due to gravity on the surface of a planet is given by $g=\frac{GM}{R^2}$.

Expressing the mass $M$ in terms of density $\rho$ and radius $R$, we have $M=\frac{4}{3}\pi R^3\rho$.

Substituting this into the expression for $g$, we get:

$g=\frac{G}{R^2}\left(\frac{4}{3}\pi R^3\rho \right)=\frac{4}{3}\pi GR\rho$

This shows that $g\propto R\rho$.

For the new planet, the density is the same as that of Earth (${\rho }_1=\rho$) and the radius is 3 times that of Earth ($R_1=3R$).

The acceleration due to gravity on the new planet is:

$g_1=\frac{4}{3}\pi G{R}_1{\rho }_1=\frac{4}{3}\pi G(3R)\rho =3\left(\frac{4}{3}\pi GR\rho \right)=3g$

Answer: $3g$