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Answer 1

hello mate✔

see the above attachment...

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Answer 2

We know that:

If two similar solid spheres are in contact, then the distance between the centres of the spheres is equal to the sum of the radius of spheres.

And:

The two spheres, where mass m and radius r in contact.

So:

The distance between centres of spheres:

$\huge{\boxed{\sf{2\:r}}}$

Now:

According to Newton's gravitational law:

$\implies$ $\sf{F = \frac{ {Gm}^{2} }{(2r) ^{2} }}$

$\implies$ $\sf{F = \frac{ {Gm}^{2} }{ {4r}^{2} }}$

Note: But both the spheres are similar.

So:

$\implies$ $\sf{d = \frac{m}{ \frac{4}{3\pi {r}^{3} } }}$

$\implies$ $\sf{m = \frac{4}{3\pi {r}^{3}.d }}$

Substituting this in the above expression:

$\implies$ $\sf{F = \frac{G( \frac{4}{3\pi {r}^{3}d }) ^{2} }{4 {r}^{2}} }$

$\implies$ $\sf{F = ( \frac{4}{9} )G {\pi}^{2} {d}^{2} . {r}^{4}}$

Here:

$\sf{( \frac{4}{9G {\pi}^{2} {d}^{2} } )}$ is constant, so let it be K.

So:

$\boxed{\sf{F\:=K.r^{4}}}$

Hence:

Force is directly proportional to radius⁴