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(B) The gravitational force $F$ between two bodies of mass $m$ separated by a distance $d$ is given by $F = \frac{G m^2}{d^2}$.Since the spheres are i

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$4$

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(B) The gravitational force $F$ between two bodies of mass $m$ separated by a distance $d$ is given by $F = \frac{G m^2}{d^2}$.Since the spheres are in contact,the distance between their centers is $d = R + R = 2R$.The mass $m$ of each sphere with density $ho$ is $m = 	ext{Volume} 	imes 	ext{Density} = \frac{4}{3} \pi R^3 ho$.Substituting these into the force equation:$F = \frac{G (\frac{4}{3} \pi R^3 ho)^2}{(2R)^2}$$F = \frac{G 	imes \frac{16}{9} \pi^2 R^6 ho^2}{4 R^2}$$F = \frac{4}{9} G \pi^2 ho^2 R^4$Since $G$,$\pi$,and $ho$ are constants,$F \propto R^4$.Therefore,$x = 4$.

If two identical spherical bodies of same material and dimensions are kept in contact,the gravitational force between them is proportional to $R^{x}$,where $x$ is a non-zero integer. [Given: $R$ is the radius of each spherical body]

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