A metal wire of uniform mass density having length L and mass M is bent to form a semicircular arc and a particle of mass m is placed at the centre of the arc. The gravitational force on the particle by the wire is:

Concept:

Gravitational Force Law: The gravitational force between two masses is given by

F = G \(\frac{m_!m_2}{r^2}\)

Where, G = is the gravitational constant,

m_1,m₂ = masses, r = distance

Calculation:

Here, \(R = \frac{L}{\pi}\)

\(g_0 = \frac{2G \frac{M}{L}}{R} = \frac{2GM\pi}{L^2}\)

\(∴ F_m = mg_0 = \frac{2GM\pi m}{L^2}\)

∴ The correct option is (4)