Math, asked by ritik12336, 1 year ago

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Answered by Anonymous
8

hello mate✔

see the above attachment...

hope it helps.... ❤

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Answered by Anonymous
13

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


Anonymous: Thank you!❤️
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