A semicircular wire has a length $L$ and mass $M$. A particle of mass $m$ is placed at the centre of

Question

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 magnitude of the gravitational force of attraction on the particle due to the wire.

Professor PC Thomas Classes · Answer

The radius $R = L/\pi$. The gravitational field at the centre of a semicircular ring is $E = \frac{2G\lambda}{R} = \frac{2G(M/L)}{L/\pi} = \frac{2\pi GM}{L^2}$. Force $F = mE = \frac{2\pi GMm}{L^2}$.