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
B
F=K/r3
C
F=K/4r2
D
F=kr2

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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