A point `P(Rsqrt(3),0,0)` lies on the axis of ring of mass M and radius R the ring is located in YZ plane with its centre at origin O A small particle of mass m starts from P and reaches O under gravitatinal attracton only its speed at O will be

Options

A. `sqrt(GM/R )`
B. `sqrt(Gm)/(R )`
C. `sqrt(Gm)/(2R)`
D. `sqrt(Gm)/(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))`
`rarr v=sqrt(2(v_(1)-v_(f))=sqrt(2)[-(GM)/(2R)+(GM)/(R )]=sqrt(GM)/(R )`