Question

Three uniform spheres each having a mass M and radius 'a' are kept in such a way that each
touch the other two. The magnitude of the gravitational force is (√3GM^2)/(Ka^2) on any of the spheres due to the other two. Find the value of K.​

Answer 1

Dear Student

The system can be considered at three particles located at the vertices of equilateral triangle having side 2a.

Gravitational force between two sphere is given as

F1 = GMM/(2a)2

As mass and radius of all sphere is same.

So on one sphere two forces of equal magnitude are acting at angle of 60o.

So resultant gravitational force on one sphere will be

F =F12+F12+2F1F1cos 60−−−−−−−−−−−−−−−−−−−−√=3F1−−−√F =3√GM24a2