JEE Main 2023 — Gravitation Question with Solution

The acceleration due to gravity at the surface of a planet can be expressed as:

$$g\propto \rho R$$

Now let's find the ratio of acceleration due to gravity at the surfaces of planets A and B:

$$\frac{g_A}{g_B}=\frac{{\rho }_A{R}_A}{{\rho }_B{R}_B}$$

Given that the densities are $$\rho$$ and $$\frac{\rho }{3}$$ and the radii are $$R$$ and $$4R$$ for planets A and B, respectively, we have:

$$\frac{g_A}{g_B}=\frac{\rho \cdot R}{\left(\frac{\rho }{3}\right)\cdot (4R)}=\frac{3}{4}$$

So, the ratio of acceleration due to gravity at their surfaces is 3 : 4