Question

Two identical solid copper spheres, of radius $R$, are placed in contact with each other. The gravitational attraction between them is proportional to -

• A. $R^2$
• B. $R^{-2}$
• C. $R^4$
• D. $R^{-4}$

Answer 1

The correct option is C $R^4$


The force of attraction between the two spheres is,

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

Here,

$m=\left(\frac{4}{3}\pi R^3\right)\rho$

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

$\Rightarrow F\propto R^4$

Hence, option $\left(C\right)$ is the correct answer.