Question

Two point masses $m$ and $4m$ are separated by a distance $d$ on a line. A third point mass $m_0$ is to be placed at a point on the line such that the net gravitational force on it is zero. The distance of that point from the mass $m$ is

• A. $\frac{d}{2}$
• B. $\frac{d}{4}$
• C. $\frac{d}{3}$
• D. $\frac{d}{5}$

Answer 1

The correct option is C $\frac{d}{3}$

Assuming mass $m_0$ is placed between the masses $m$ and $4m$, and distance of $m_0$ from $m$ is $r$.


Force of gravitation on $m_0$ due to $m$ is given by

$F_1=\frac{G\left(m\right)\left(m_0\right)}{r^2}$

Force of gravitation on $m_0$ due to $4m$

$F_2=\frac{G\left(4m\right)\left(m_0\right)}{(d-r{)}^2}$

Since, net force experienced by $m_0$ is zero.

$\Rightarrow F_1=F_2$

$\Rightarrow \frac{Gm{m}_0}{r^2}=\frac{G4m{m}_0}{(d-r{)}^2}$

$\Rightarrow d-r=\pm 2r$

Taking positive value, since with negative value the third point mass won't be on line.

$\Rightarrow d=3r$

Thus, $r=\frac{d}{3}$

Hence, option $\left(c\right)$ is correct..