QJEEM23Ph88a5: JEE Main 2023 Physics - Class 11 JEEM23Ph88a5 Solution: The radii of two planets 'A' and 'B' are 'R' and '4R' and their …

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