A point `P(R sqrt(3),0,0)` lies on the axis of a ring of mass M and radius R. The ring is located in yx-plane with its centre at origin O. A small particle of mass `m` starts from P and reaches O under gravitational attraction only. Its speed at O will be

Options

A. `sqrt((GM)/(R))`
B. `sqrt((Gm)/(R))`
C. `sqrt((GM)/(2R))`
D. `sqrt((2m)/(sqrt(2)R))`

Answer

A

Explanation

Increase in kinetic energy = decrease in potential energy

or `(1)/(2)mv^(2)=U_(i)-U_(f)=m(V_(i)-V_(f))`
or `v=sqrt(2(V_(i)-V_(f)))=sqrt(2[1-(GM)/(2R)+(GM)/(R)])=sqrt((GM)/(R))`