Gravitational force on one of three touching spheres – Rankers Physics
Topic: Gravitation
Subtopic: Newton's Law of Gravitation

Gravitational force on one of three touching spheres

If three uniform spheres, each having mass \(M\) and radius \(r\), are kept in such a way that each touches the other two, the magnitude of the gravitational force on any sphere due to the other two is
\(\frac{GM^2}{4r^2}\)
\(\frac{2GM^2}{r^2}\)
\(\frac{2GM^2}{4r^2}\)
\(\frac{\sqrt{3} GM^2}{4r^2}\)

Solution:

The distance between centers is \(2r\). Force between any two is \(F = \frac{GM^2}{4r^2}\). Since the angle between the forces is \(60^\circ\), the resultant force is \(F_{\text{net}} = \sqrt{3}F = \frac{\sqrt{3} GM^2}{4r^2}\).

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