Two spheres of radius R are placed in contact | vedclass

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(B) The mass $M$ of each sphere is given by the product of its volume and density: $M = V \cdot \rho = (\frac{4}{3} \pi R^3) \rho$.The distance betwee

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$\frac{4}{9}{\pi ^2}{\rho ^2}{R^4}G$

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(B) The mass $M$ of each sphere is given by the product of its volume and density: $M = V \cdot \rho = (\frac{4}{3} \pi R^3) \rho$.The distance between the centers of the two spheres in contact is $d = R + R = 2R$.According to Newton's law of gravitation,the force $F$ between two point masses is $F = \frac{G M_1 M_2}{d^2}$.Substituting the values: $F = \frac{G (\frac{4}{3} \pi R^3 \rho) (\frac{4}{3} \pi R^3 \rho)}{(2R)^2}$.$F = \frac{G \cdot \frac{16}{9} \pi^2 R^6 \rho^2}{4 R^2}$.$F = \frac{16}{36} \pi^2 \rho^2 R^4 G = \frac{4}{9} \pi^2 \rho^2 R^4 G$.

Two spheres of radius $R$ are placed in contact as shown in the figure. If the mass density of each sphere is $\rho$,find the gravitational force between them.

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