The gravitational force between two identical | vedclass

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(A) Let the density of the gold spheres be $ho$. The mass $m$ of each sphere is given by $m = ho 	imes \frac{4}{3} \pi r^3$.When the two spheres

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$r^4$

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(A) Let the density of the gold spheres be $ho$. The mass $m$ of each sphere is given by $m = ho 	imes \frac{4}{3} \pi r^3$.When the two spheres are in contact,the distance between their centers is $d = r + r = 2r$.The gravitational force $F$ between them is given by Newton's law of gravitation: $F = \frac{G m^2}{d^2}$.Substituting the values of $m$ and $d$:$F = \frac{G (ho 	imes \frac{4}{3} \pi r^3)^2}{(2r)^2}$$F = \frac{G ho^2 	imes \frac{16}{9} \pi^2 r^6}{4r^2}$$F = G ho^2 	imes \frac{4}{9} \pi^2 r^4$Since $G$,$ho$,and $\pi$ are constants,we have $F \propto r^4$.

The gravitational force between two identical uniform solid gold spheres of radius $r$ placed in contact is proportional to:

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