A ring of radius `R = 4m` is made of a highly dense material. Mass of the ring is `m_(1) = 5.4 xx 10^(9) kg` distributed uniformly over its circumference. A highly dense particle of mass `m_(2) = 6 xx 10^(8) kg` is placed on the axis of the ring at a distance `x_(0) = 3 m` from the centre. Neglecting all other forces, except mutual gravitational interacting of the two. Caculate
(i) displacemental of the ring when particle is at the centre of ring, and
(ii) speed of the particle at that instant.

Options

A. `(i)0.4 m(ii) 16 cms^(-1)`
B. `(i) 0.3 m (ii) 18 cm//s`
C. `(i) 0.2 m (ii) 12 cm//s`
D. `(i) 0.6 m (ii) 24 cm//s`

Answer

B

Explanation

(a) Let `x` be the displacement of ring. Then displacement of the particle is `x_(0)-x`, or `(3.0-x)m`. Centre of mass will not move. Hence, `(5.4xx10^(9))x=(6xx10^(8))(3-x)` solving, we get `x=0.3m`