Question

Two identical spheres are placed in contact with each other. The force of gravitation between the spheres will be proportional to (R = radius of each sphere )

• A. R
• B. $R^3$
• C. $R^4$
• D. None of these

Answer 1

Answer: (C)

$R^4$

Gravitation force between them, $F=\frac{G{m}_1{m}_2}{R^2}$

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

$F\propto R^4$

Hence, force is directly proportional to $R^4$