Find potential at a point 'P' at a distance 'x' on the axis away from centre of a uniform ring of mass `M` and radius `R` .

Explanation

Ring can be considered to be made of large number of point masses `(m_(1) ,m_(2)…..etc)`
`V_(P) = - (Gm_(1))/(sqrt(R^(2)+x^(2)))-(Gm_(2))/(sqrt(R^(2)+x^(2)))-...`
`=-(G)/(sqrt(R^(2)+x^(2)))(m_(1)+m_(2)...)=-(GM)/(sqrt(R^(2)+x^(2)))`,where`M=m_(1)+m_(2)+m_(3)`+....
Potential at centre of ring `= - (G.M)/(R)`
.