Question 130: Gravitation

Question

The radii of two planets A and B are in the ratio 2 : 3. Their densities are 3$\rho$ and 5$\rho$ respectively. The ratio of their acceleration due to gravity is :

Accepted Answer

Given,
${{{r_A}} \over {{r_B}}} = {2 \over 3}$
${{{ho _A}} \over {{ho _B}}} = {3 \over 5}$
We know,
Acceleration due to gravity
$g = {{GM} \over {{r^2}}} = {G \over {{r^2}}} 	imes {4 \over 3}\pi {r^3} 	imes ho $
$ = {{4\pi Grho } \over 3}$
$	herefore$ $g \propto ho r$
$	herefore$ ${{{g_A}} \over {{g_B}}} = {{{ho _A}} \over {{ho _B}}} 	imes {{{r_A}} \over {{r_B}}}$
$ = {3 \over 5} 	imes {2 \over 3}$
$ = {2 \over 5}$

Answer

9 : 4

Answer

9 : 8

Answer

9 : 10

Answer

2 : 5

Gravitation

The radii of two planets A and B are in the ratio 2 : 3. Their densities are 3\rho and 5\rho respectively. The ratio of their acceleration due to gravity is :

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