Question

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

• A. $6m$ from $8kg$
• B. $3m$ from $8kg$
• C. $6m$ from $2kg$
• D. $4.5m$ from each mass

Answer 1

The correct option is A $6m$ from $8kg$

Let the gravitational field is zero at a distance $x$ from 2 kg mass and distance $(9-x)$ from 8 kg mass.

Thus, $\frac{G{m}_1}{x^2}=\frac{G{m}_2}{(9-x{)}^2}$

or $\frac{G\left(2\right)}{x^2}=\frac{G\left(8\right)}{(9-x{)}^2}$

or $4x^2=(9-x{)}^2$

or $2x=9-x$ or $x=3m$

Thus, field is zero at 3 m from 2kg and 6 m from 8 kg.