Question

Three equal masses $m$ are placed at the three vertices of an equilateral triangle of side $a$. The gravitational force exerted by this system on another particle of mass $m$ placed at the mid-point of a side is :

• A. $\frac{{Gm}^2}{{3a}^2}$
• B. $\frac{{4Gm}^2}{{3a}^2}$
• C. $\frac{{Gm}^2}{a^2}$
• D. $\frac{{3Gm}^2}{a^2}$

Answer 1

The correct option is B $\frac{{4Gm}^2}{{3a}^2}$

Force in $OA=\frac{4G{m}^2}{a^2}$

Force in $OB=\frac{4G{m}^2}{a^2}$

As equal and opposite forces cancel each other

Force in $OC=\frac{G{m}^2}{\left[\right(\sqrt{3}/2)a{]}^2}=\frac{4G{m}^2}{3a^2}$

So net gravitational force on $m=\frac{4G{m}^2}{3a^2}$