A semicircular wire has a length L and mass M. A particle of mass m is placed at the Centre of the circle. Find the gravitational attraction on the particle due to the wire.

Question

Philoid · Accepted Answer

Let the radius of the wire be R. Given, length of the wire is L and mass is M. Mass of the particle is

Let us take a small element on the wire. The arc length of the element is . Therefore, mass of the element,

Also, therefore,

The force on particle due to element is

The horizontal components of force cancel out.

therefore,

in the positive y direction.