Two planets A and B of radii R and 1.5 R have densities ρ and ρ / 2 respectively. ratio of acceler

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7.Gravitation

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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 :

A

$2: 3$

B

$2: 1$

C

$3: 4$

D

$4: 3$

(JEE MAIN-2023)

Solution

$g =\frac{ GM }{ R ^2}=\frac{4}{3} \pi G \rho R$

$\therefore \frac{ g _2}{ g _1}=\frac{\rho_2}{\rho_1} \times \frac{ R _2}{ R _1}=\frac{1}{2} \times 1.5=\frac{3}{4}$

Standard 11

Physics

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