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7.Gravitation
medium
The radii of two planets $A$ and $B$ are $R$ and $4 R$ and their densities are $\rho$ and $\rho / 3$ respectively. The ratio of acceleration due to gravity at their surfaces $\left(g_A: g_B\right)$ will be
A
$1: 16$
B
$3: 16$
C
$3: 4$
D
$4: 3$
(JEE MAIN-2023)
Solution
$g=\frac{G M}{R^2}=\frac{G}{R^2} \times \rho \times \frac{4 \pi}{3} R^3=\left(\frac{4 \pi}{3} G\right) \rho R$
$\frac{g_A}{g_B}=\frac{R \times \rho}{4 R \times \frac{\rho}{3}}=\frac{3}{4}$
Standard 11
Physics
