Two planets A and B of radii R and 1.5 R have densities $\rho$ and $\rho / 2$ respectively. The ratio of acceleration due to gravity at the surface of B to A is :
Select the correct option:
A
2 : 3
B
2 : 1
C
3 : 4
D
4 : 3
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution
$\begin{aligned} & g=\frac{G M}{R^2}=\frac{4}{3} \pi G \rho R \\ & \therefore \frac{g_2}{g_1}=\frac{\rho_2}{\rho_1} \times \frac{R_2}{R_1}=\frac{1}{2} \times 1.5=\frac{3}{4}\end{aligned}$
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