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Question

Two metal spheres of the same material and radius $$r$$ are in contact with each other. The gravitational force of attraction between the spheres is given by:


A
F=Kr4
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B
F=K/r3
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C
F=K/4r2
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D
F=kr2
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Solution

The correct option is A $$F= Kr^{4}$$
Mass of each metal sphere is given by:
$$m= \dfrac{4}{3}\pi r^{3}\rho$$

The force of attraction between two metal sphere is given by:
$$F = \dfrac{Gmm}{(2r)^2}$$
$$F = \dfrac{G(\dfrac{4}{3}\pi r^{3}\rho)(\dfrac{4}{3}\pi r^{3}\rho)}{4r^2}$$
$$F = \dfrac{G(\frac{4}{3}\pi \rho)(\dfrac{4}{3}\pi \rho)}{4}\dfrac{(r^3)(r^3)}{r^2}$$
$$F = K r^4$$

Physics

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