A ring of radius R is made from a thin wire of radius r. If `rho` is the density of the material of wire then what will be the gravitational force exerted by the ring on the material particle of mass m placed on the axis of ring of ring at a distance x from its centre. Shown that the force will be maximum when `x=R//sqrt(2)` and the maximum value of force will be given as
`F_(max)=(4pi^(2)G r^(2)rhom)/((3)^(3//2)R^(2))`

Explanation

`(da)/(dx) = 0` for `a_("max") rArr x = (R )/(sqrt(2))`