Question

Consider two solid uniform spherical objects of the same density $\rho$. One has radius $R$ and the other has radius $2R$. They are in outer space where the gravitational fields from other objects are negligible. If they are arranged with their surface touching, what is the contact force between the objects due to their traditional attraction?

• A. $G{\pi }^2{R}^4$
• B. $\frac{128}{81}G{\pi }^2{R}^4{\rho }^2$
• C. $\frac{128}{81}G{\pi }^2$
• D. $\frac{128}{87}G{\pi }^2{R}^2$

Answer 1

The correct option is B $\frac{128}{81}G{\pi }^2{R}^4{\rho }^2$

Since the spheres are touching, distance between their centers=$r=R+2R=3R$.

Mass of sphere of radius R$=\rho \frac{4}{3}\pi (R{)}^3$

Mass of sphere of radius 2R$=\rho \frac{4}{3}\pi (2R{)}^3$

Force of attraction between the spheres=$\frac{G{M}_1{M}_2}{r^2}$

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

$=\frac{128}{81}G{\pi }^2{R}^4{\rho }^2$.