Question

Two rings of radii r and mass M are kept at a distance r apart, such that their planes are parallel to each other. A point particle of mass m/2 is kept at the centre of one of the rings. The net force experienced by the particle will be

• A. $G{m}^2/2r^2$
• B. Zero
• C. $\frac{G{m}^2}{4\sqrt{(}2)a^2}$
• D. $2G{m}^2/r^2$

Answer 1

The correct option is C $\frac{G{m}^2}{4\sqrt{(}2)a^2}$

If the particle was present at the centre of the first ring, then force exerted by the ring on this particle will be zero.
The gravitational force due to the ring at a distance r from the centre along the axis is given by $F=\frac{GMmr}{(a^2+r^2{)}^{1.5}}$, a is the radius of the ring and r is the distance between the centres of the ring.
Substituting r=a, we get, $F=\frac{G{m}^2}{4\sqrt{(}2)a^2}$
Thus option (c) is the correct option