Question

Gravitational force between two point masses m and M separated by a distance r is F. Now if a point mass $3$m is placed next to m, what will be the (a) force on M due to m, (b) total force on M?

• A. $F=4F$.
• B. $F=5F$.
• C. $F=6F$.
• D. $F=7F$.

Answer 1

The correct option is A $F=4F$.

a. If r is the distance between two point masses m and M, then the gravitational force on m due to mass M is F $=$ GMm/$r^2$. Since the gravitational force between two point masses is independent of the presence of other masses, so if a point mass $3$m is placed next to m, the force on M due to m is $F=\frac{GMm}{r^2}$
b. Total force on the body of mass M is F, i.e.,
$F=\frac{GM\times (m+3m)}{r^2}=\frac{4GMm}{r^2}=4F$.