Question

A wire of length L and mass m is bent in to an arc of a circle, subtending an angle of 60 degrees at the centre. Determine the gravitational potential at the centre of the circle of which the arc forms a part

• A. $GM\pi /L$
• B. $2GM\pi /L$
• C. $2GM\pi /3L$
• D. $GM\pi /3L$

Answer 1

The correct option is D $GM\pi /3L$

The length of the arc is $L=\left(\pi /3\right)R$.
The radius of the arc is $R=\left(3L/\pi \right)$.
The potential due to the arc is $V=GM/R=GM\pi /3L$
The correct option is (d)