Question

Two bodies of masses $2 \, kg$ and $8 \, kg$ are separated by a distance of $9 \, m$ . The point where the resultant gravitational field intensity is zero is at a distance of

• A. $4.5m$ from each mass
• B. $6 \, m$ from $2 \, kg$
• C. $6m$ from $8kg$
• D. $2.5m$ from $2kg$

Answer 1

Answer: (C)

If $x$ is the distance of point on the line joining the two masses from mass $m_{2}′$ where gravitational field intensity is zero, then
$\frac{G m}{\left(r - x\right)^{2}}=\frac{G m_{2}}{x^{2}}$ or $\frac{2}{\left(9 - x\right)^{2}}=\frac{8}{x^{2}}$
or $\frac{1}{9 - x}=\frac{2}{x}$
On solving, $x=6 \, m$