Question 146: 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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