Three equal masses, m each are placed at the three corners of an equilateral triangle of side length l. The gravitational field at centre of triangle is

When three equal masses, each of mass m , are placed at the corners of an equilateral triangle with a side length l , the gravitational field at the center of the triangle is zero because of the symmetrical arrangement of the masses. Each mass generates a gravitational field that points toward itself.

At the centroid, equidistant from every corner of the triangle, the gravitational fields created from each mass can be weighed. Since the masses were equal and symmetrically placed, the magnitudes of the gravitational fields which they created were identical in magnitude. However, their directions were such as to point toward each corresponding mass.

At the centroid, when the vector sums of gravitational fields of three masses are taken, then these cancel out each other completely. This happens as the angles between lines drawn connecting each mass and the centroid are all the same so that vectors pointing out of each pair of masses would add to point in opposite directions.

Thus, the net gravitational field at the center of the triangle becomes zero. This result shows an important concept in physics: symmetry can cause cancellation effects, leading to a balanced state in gravitational interactions.