Question

Two point masses having mass $m$ and $2m$ are placed at separation distance $d$. The point on the line joining point masses,where gravitational field intensity is zero will be at distance

• A. $\frac{2d}{\sqrt{3}+1}$ from point mass $\text{"2m"}$
• B. $\frac{2d}{\sqrt{3}-1}$ from point mass $\text{"2m"}$
• C. $\frac{d}{1+\sqrt{2}}$ from point mass $\text{"m"}$
• D. $\frac{d}{1-\sqrt{2}}$ from point mass $\text{"m"}$

Answer 1

The correct option is C $\frac{d}{1+\sqrt{2}}$ from point mass $\text{"m"}$

Let $r$ be the distance of the point from $m$ where the gravitational field is zero.


The field due to $m$ will be cancelled by the field due to $2m$.

Hence, $E_m=E_{2m}$

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

$\Rightarrow \frac{1}{r}=\pm \frac{\sqrt{2}}{d-r}$

$\Rightarrow d-r=+\sqrt{2r}$

$\Rightarrow r(1+\sqrt{2})=d$

$\Rightarrow r=\frac{d}{1+\sqrt{2}}$

Hence, option (c) is the correct answer.

$\text{Key Concept:}$ Between two masses, there will be a point where the gravitational field of one mass will be equal and opposite to the gravitational field of the other mass. $\text{Why this question:}$ To make students familiar with the concept of gravitational field intensity.