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(A) The mass $M$ of a solid sphere of radius $R$ and density $ho$ is given by $M = 	ext{Volume} 	imes 	ext{Density} = \frac{4}{3} \pi R^3 ho$.S

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$F \propto R^4$

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(A) The mass $M$ of a solid sphere of radius $R$ and density $ho$ is given by $M = 	ext{Volume} 	imes 	ext{Density} = \frac{4}{3} \pi R^3 ho$.Since both spheres are made of the same material,their density $ho$ is constant.Thus,$M \propto R^3$.The distance between the centers of the two spheres in contact is $d = R + R = 2R$.The gravitational force $F$ between two spheres is given by Newton's Law of Gravitation: $F = \frac{G M_1 M_2}{d^2}$.Substituting $M_1 = M_2 = M$ and $d = 2R$,we get $F = \frac{G M^2}{(2R)^2} = \frac{G M^2}{4R^2}$.Since $M \propto R^3$,then $M^2 \propto (R^3)^2 = R^6$.Substituting this into the force equation: $F \propto \frac{R^6}{R^2} = R^4$.Therefore,$F \propto R^4$.

Two solid spheres each of radius $R$ made of the same material are placed in contact with each other. If the gravitational force acting between them is $F$,then:

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