Physics - Gravitation Question with Solution | TestHub

The mass of each copper sphere is given by the product of its volume and density:

$m=\frac{4}{3}\pi R^3\varrho$

Since the two identical spheres are placed in contact with each other, the distance between their centers is $d=2R$.

The gravitational force between the two spheres is:

$F=\frac{G{m}_1{m}_2}{d^2}=\frac{G{m}^2}{(2R{)}^2}$

Substituting the expression for mass $m$:

$F=\frac{G{\left(\frac{4}{3}\pi R^3\varrho \right)}^2}{4R^2}$

$F=\frac{G\left(\frac{16}{9}{\pi }^2{R}^6{\varrho }^2\right)}{4R^2}$

$F=\frac{4}{9}G{\pi }^2{\varrho }^2{R}^4$

From the above expression, it is clear that the gravitational force $F$ is proportional to $R^4$.

Therefore, $x=4$.

Answer: $4$