Calculate gravitational field intensity at a distance x on the axis from centre of a uniform disc of mass `M` and radius `R` .

Explanation

Consider a elemental ring of radius r and thickness dr on surface of disc as shown in figure

Gravitational field due to elemental ring
`dE=(GdMx)/((x^(2)+r_(2))^(3//2))` Here `dM=(M)/(piR_(2)).2pirdr=(2M)/(R^(2))rdr`
`:.dE = (G.2 Mxrdx)/(R^(2)(x^(2)+r^(2))^(3//2))`
`:.E=underset(0)overset(R)int((2GMx)/(R^(2)))(rdr)/((x^(2)+r^(2))^(3//2))`
`:. E = (2GMx)/(R^(2))[(1)/(x)-(1)/(sqrt(x^(2)+R^(2)))]`