Question

A ring of radius R = 4 m is made of a highly dense material. Mass of the ring is m₁ = 5.4 x 10⁹ kg distributed uniformly over its circumference. A highly dense particle of mass m₂ = 6 x 10⁸ kg is placed on the axis of the ring at a distance x₀ = 3 m from the centre. Neglecting all other forces, except mutual gravitational interaction of the two. Calculate :

(i) displacement of the ring when particle is at the centre of ring, and 

(ii) speed of the particle at that instant.

Answer 1

(a) Let x be the displacement of ring. Then displacement of the particle is x₀ - x, or (3.0 - x) m. Centre of mass will not move. Hence,

(b) Apply conservation of linear momentum and conservation of mechanical energy.