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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 :
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$3: 4$
Acceleration due to gravity,
$\mathrm{g}=\frac{\mathrm{GM}}{\mathrm{R}^2}=\frac{4}{3} \pi \mathrm{G} \rho \mathrm{R}$
$\therefore \frac{g_2}{g_1}=\frac{\rho_2}{\rho_1} \times \frac{R_2}{R_1}=\frac{1}{2} \times 1.5=\frac{3}{4}$
$\mathrm{g}=\frac{\mathrm{GM}}{\mathrm{R}^2}=\frac{4}{3} \pi \mathrm{G} \rho \mathrm{R}$
$\therefore \frac{g_2}{g_1}=\frac{\rho_2}{\rho_1} \times \frac{R_2}{R_1}=\frac{1}{2} \times 1.5=\frac{3}{4}$
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