Use the formula for surface gravity

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

Write mass in terms of density

For a spherical planet, $M = \frac{4}{3}\pi R^3 \rho$

Substituting into the formula for $g$: $g = \frac{G\left(\frac{4}{3}\pi R^3 \rho\right)}{R^2}$ $g = \frac{4}{3}\pi G R \rho$

So, $g \propto R\rho$

For planet A

Radius $= R$, density $= \rho$ $g_A \propto R\rho$

For planet B

Radius $= 1.5R$, density $= \frac{\rho}{2}$ $g_B \propto (1.5R)\left(\frac{\rho}{2}\right)$ $g_B \propto 0.75R\rho$

Find the ratio

$\frac{g_B}{g_A} = \frac{0.75R\rho}{R\rho} = 0.75 = \frac{3}{4}$

Hence, $g_B : g_A = 3 : 4$

Check options

The correct option is D: $3:4$.

Compare with stored answer

Stored correct answer is D, which matches our derived answer.