Question 272: Gravitation

Question

Two planets A and B have densities ' $\rho_1$ ', ' $\rho_2$ ' and have radii ' $r_1$ ', ' $r_2$ ', respectively. The ratio of acceleration due to gravity on $A$ to that of $B$ is

Accepted Answer

We know,
$$ g=\frac{G M}{R^2} $$
If the density is $ho$, then
$$ \begin{array}{ll} \Rightarrow  \mathrm{M}=\frac{4}{3} \pi \mathrm{R}^3 ho \quad \ldots(\because \mathrm{M}=\mathrm{V} 	imes \mathrm{d}) \ 	herefore \quad \mathrm{g} =\frac{4}{3} \pi \mathrm{GR} ho \end{array} $$
From given,
$$ \begin{aligned} \mathrm{g}_{\mathrm{A}} & =\frac{4}{3} \pi \mathrm{Gr}_1 ho_1 \ \mathrm{~g}_{\mathrm{B}} & =\frac{4}{3} \pi \mathrm{Gr}_2 ho_2 \end{aligned} $$
Therefore,
$$ \frac{g_A}{g_B}=\frac{r_1}{r_2} 	imes \frac{ho_1}{ho_2} \Rightarrow \frac{g_A}{g_B}=\frac{r_1 ho_1}{r_2 ho_2} $$

Answer

$r_1: r_2$

Answer

$r_1 \rho_1: r_2 \rho_2$

Answer

$\quad r_1^2 \rho_1: r_2^2 \rho_2$

Answer

$r_1 \rho_2: r_2 \rho_1$

Gravitation

Two planets A and B have densities ' \rho_1 ', ' \rho_2 ' and have radii ' r_1 ', ' r_2 ', respectively. The ratio of acceleration due to gravity on A to that of B is

Choose the correct answer: