If a particle of mass m is moving in a horizontal circle of radius r with a centripetal force ` (-1//r^(2))` , the total energy is

Options

A. `-(4)/(r) `
B. `-(2)/(r) `
C. `-(1)/(r)`
D. `-(1)/(2r)`

Answer

D

Explanation

`(mv^(2))/(r)=(1)/(r^(2)) i.e., mv^(2)=(1)/(r)`
`:. K.E. =(e^(2))/(2r) and P.E.= intF dtr=-(e^(2))/(r)`
`:.` Total energy =K.E. + P.E.`=(e^(2))/(2r)-(e^(2))/(r)=-(e^(2))/(2r)`