Question

A ring of maas m1 and radius R is fixed in space at some location. An external agent rings a a point m2 from infinity To centre of the Ring. the work done by the external agent will be

Answer 1

Answer

All point on the circumference of the ring are at distance R2+x2

​from the center O of the ring.

Force on the mass m at P : F=R2+x2GMm​×(2cosθ) where cosθ=R2+x2

​x​

Due to symmetry, vertical components of the forces from two symmetrical elements cancel out, the horizontal components add up, hence we get a factor of 2.

∴F=R2+x2GMm​×2R2+x2

​x​

When F is maximum, dxdF​=0

⇒(R2+x2)−23​+x(−23​(R2+x2)−23​−1×2x=0

⇒(R2+x2)=3x2

⇒x=2

​R​