Derive an expression for the gravitational field due to a uniform rod of length L and mass M at a point on its perpendicular bisector at a distance d from the center.

Here, the mass of the rod is and the length is .

Let us take an element of length dx at a distance x from the center of the rod.

Mass of the element is

The element is at a distance d from the rod.

The horizontal components cancel out and the field is in the negative y direction given by

—————(1)

We know,

—————(2)

Substituting (2) in (1)

Which gives us