A point P lies on the axis of a ring of mass M and radius a, at a distance a - Physics - Gravitation

Question

A point P lies on the axis of a ring of mass M and radius a, at a
distance a from its centre C A small particle starts from P and
reaches C under gravitational attraction only Its speed at C will
be
(A) 2 GM a (B) 2 GM a 1 - 1 2 (C) 2 GM a 2 - 1 (D) zero

Shobhit Mittal · Accepted Answer

Dear student,

let the point mass be m
gravitational potential energy at axis is defined asE=-GMma2+r2  here r=aEa=-GMma2+a2=-GMma2potential at center be Ec=-GMma change of potential energy is =-ve of work done-GMma +GMma2=GMma21-2work done=GMma22-1work done is change in kEGMma22-1=12mv22GMa2-1=v2v=2GMa2-1=2GMa1-12  option B is correct
Regards

A point P lies on the axis of a ring of mass M and radius a, at a distance a from its centre C. A small particle starts from P and reaches C under gravitational attraction only. Its speed at C will be (A) 2 GM a (B) 2 GM a 1 - 1 2 (C) 2 GM a 2 - 1 (D) zero