A uniform thin rod of mass m and length l is bent into a semicircle. Gravitational field intensity at the centre O is :

Let the mass per unit length of the wire be λ=ml=mπR, where R is the radius of the circle.Thus horizontal components of the gravitational field intensity at the center cancel each other.The vertical component of the same = ∫−π/2π/2 G(λRdθ)R2cos⁡θ=2GmπR2=2πGml2