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:
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Question

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:

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G1 Physics · Accepted Answer

For the semicircular wire: L = πR Therefore, R = L/π The gravitational field at the centre of a uniform semicircular arc is: g₀ = 2GM/(LR) Substituting R = L/π: g₀ = 2πGM/L² Hence force on mass m is: F = mg₀ = 2πGmM/L²