Find the gravitational field strength at the centre of a thin semicircular ring of radius R and total mass M. Its linear mass density is λ = M/(πR).

Question

G1 Physics · Accepted Answer

For a mass element dm = λR dφ on the semicircle, dE = Gdm/R² = (Gλ/R)dφ. Components perpendicular to the symmetry axis cancel. Along the symmetry axis, E = (Gλ/R)∫₀^π sinφ dφ = 2Gλ/R = 2GM/(πR²). Correct answer: C.