Two spheres are separated by a known distance and we need to know the angle which the strings will make with the vertical due mutual attraction of the spheres and the problem as shown in the diagram below.

Two spheres are separated by a known distance and we need to know the angle which the strings will make with the vertical  due mutual attraction of the spheres and the problem as shown in the diagram below.

Solution

As the strings turn tight, tension is developed in the string and it can be resolved into components. By dividing the two equations, we can solve the problem as shown in the diagram below.