A circular ring of mass M and radius R and a spherical shell of mass 3M and radius R are arranged such that their centers are separated by a distance 3R and the plane of the circular ring is perpendicular to the line joining the centers. Gravitational field intensity at a point at a distance ‘R’ from the center of the ring is 

Let P be the point of interest. Gravitational field at ‘P’ due to circular ring.
 $$\begin{gathered} E_1=\frac{GMx}{{(x^2+R^2)}^{{\displaystyle \frac{3}{2}}}} \\ here x=dis\tan ce of the point from center of the ring; R=radius of the ring \\ \Rightarrow E_1=\frac{GMR}{{\left(R^2+R^2\right)}^{3/2}}=\frac{GMR}{2\sqrt{2}{R}^3}=\frac{GM}{2\sqrt{2}{R}^2} \end{gathered}$$
Gravitational field at ‘P’ due to spherical shell

  $E_2=\frac{3GM}{{\left(2R\right)}^2}=\frac{3GM}{4R^2}$  

$\therefore$Net gravitational field at a point ‘P’ is 
$E_{net}=E_2-E_1\left[\because E_2>E_1\right]$  towards center of spherical shell.
$E_{net}=\frac{3GM}{4R^2}-\frac{GM}{2\sqrt{2}{R}^2}$ 
$E_{net}=\frac{GM}{R^2}\left[\frac{3}{4}-\frac{1}{2\sqrt{2}}\right]$ towards center of spherical shell.