Question

Two metal spheres of equal radius R and equal densities are touching each other the force of attraction f between them is proportional to

Answer 1

attraction force between metal sphere is given by f = GMM/(2R)²
because separation between centre of the spheres is (R + R) = 2R

now, f = GM²/4R²

but given densities of both spheres are equal.
Let density of each sphere is $\rho$
then, mass, M = $\frac{4}{3}\pi R^3\rho$

so, f = $\frac{G\frac{16}{9}\pi^2R^6\rho^2}{4R^2}$

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

Here it is clear that force is directly proportional to R⁴ .