Question

Two lead spheres of same radius are in contact with each other. The gravitational force of attraction between them is F. If two lead spheres of double the previous radius are in contact with each other, the gravitational force of attraction between them will be:

• A. $2F$
• B. $32F$
• C. $8F$
• D. $16F$

Answer 1

The correct option is D $16F$

$F=\frac{G{M}_1{M}_2}{R^2}$
$M=\rho \times \frac{4}{3}\pi R^3$
$\therefore M\propto R^3$
$\therefore F\propto R^4$
$\therefore$ If radius doubles, force becomes $2^4$ times i.e. $16$ times.