Question 13: Gravitation

Question

Two spheres of the same material and same radii r are touching each other. The gravitational force between the spheres is proportional to

Accepted Answer

The two spheres are touching each other as shown below.
Let m be the mass of each sphere.
Gravitational force between the spheres,
$$F = G{{m.m} \over {{{(2r)}^2}}} = G.{{{m^2}} \over {4{r^2}}}$$
$$ = G.{{{{\left[ {{4 \over 3}\pi {r^3}.ho } ight]}^2}} \over {4{r^2}}}$$ [Mass = volume $$	imes$$ density]
$$ = {{4G{\pi ^2}{r^6}{ho ^2}} \over {3 	imes 4{r^2}}}$$
$$ \Rightarrow F = \left( {{{4G{\pi ^2}{ho ^2}} \over 3}} ight){r^4} \Rightarrow F \propto {r^4}$$

Answer

$${1 \over {{r^2}}}$$

Answer

r2

Answer

$${1 \over {{r^4}}}$$

Answer

r4

Gravitation

Two spheres of the same material and same radii r are touching each other. The gravitational force between the spheres is proportional to

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