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Newtons universal law of gravitation states that

$$F=\dfrac{GMm}{d^{2}}$$

where $d$ is the distance between the center of mass of the two masses. Now a ring's center of mass is not in the ring. So if we put a sphere's center of mass in the ring's center of mass, then $d=0$ and gravitational force will be infinite. This isn't right. So where am I wrong?

Please comment if I couldn't make my question clear enough.

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    $\begingroup$ Consider the direction of forces from all the parts of the ring and how they cancel out. $\endgroup$
    – StephenG - Help Ukraine
    Commented Aug 11, 2018 at 8:19
  • $\begingroup$ Yeah I also have confusion regarding d = 0 .....if we touch two masses d is almost 0 then wont the force be too large. Then this means we dont actually touch anything but experience the force in the form of touch. $\endgroup$
    – Mitul Agrawal
    Commented Mar 5, 2020 at 17:35

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Newton's law is for point masses, not for extended bodies. Here you should consider the sum of all forces by all individual point masses of the ring in the center, that is resultant force. It's simple to see all forces vanished each other. Therefore resultant force is zero at the ring center.

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  • $\begingroup$ So d is the distance between the center of masses isn't always right? $\endgroup$
    – Theoretical
    Commented Aug 15, 2018 at 17:01
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Newton’s law of Gravitation is for particles, where the size of objects is negligible compared to distance between them. Here you can use superposition principle and integrate over small elements of objects. In the case you asked it would be a zero force due to symmetry. Newton’s law doesn’t state about centers of mass of objects.But sphere’s center of mass would work in many cases

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