Consider a ring of mass “M” as shown below. What is the gravitational potential at a point “p” at a distance of “r” from the centre of the ring?
Answer & explanation
Correct answer: option 1
Consider an element od mass “dm” of the ring at a distance “z” from the point “p”.
The gravitational potential (dV) due to this elemental mass at point “p” is;
dV = -(G*dm)/z
Integrating dV for the whole ring of mass “M”, we get;
V = -(G*M)/z
From Pythagorean theorem, we get;
z = (a2+r2)1/2
Therefore; V = -(G*M)/(a2+r2)1/2.