Physics - Gravitation Question with Solution | TestHub

The distance from each corner to the center of the square is $r=\frac{\sqrt{a^2+a^2}}{2}=\frac{a\sqrt{2}}{2}=\frac{a}{\sqrt{2}}$. The gravitational field intensity due to each mass $m$ at the center is $E=\frac{Gm}{r^2}=\frac{Gm}{(a/\sqrt{2}{)}^2}=\frac{2Gm}{a^2}$. Since the masses are identical and placed symmetrically at the corners of a square, the gravitational field vectors due to diagonally opposite masses at the center are equal in magnitude and opposite in direction, thus they cancel each other out. Therefore, the net gravitational field intensity at the center of the square is zero.