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A particle of mass m is moving is a hori...

A particle of mass `m` is moving is a horizontal circle of radius `x` under a centripetal force equal to `- (kv^(2))` where it is constant The total energy of the particle is

A

`-(k) /(r )`

B

`-(k)/(2r )`

C

`(k)/(2r)`

D

`(2k)/(r )`

Text Solution

Verified by Experts

The correct Answer is:
B
Since the particle is moving in horizontal circle exectripetal force
`F = (mv^(2))/(r ) = (k)/(y^(2))…..(i)`
`(mv^(2)) = (k)/(r )`
kinetic enrgy of the particle
`K = (1)/(2) mv^(2) = (k)/(2r)(Using (i))`
As `F = (-dU)/(dv)`
`:.` Potential energy
`U=-underset(infty)overset(r)intFdr=- underset(infty)overset(r)int r^(-r)dr=((-k)/(r^(2)))dr=Kdr=(-k)/(r)`
`:.` Total `"energy "=K+U=(k)/(2r)-(k)/(r)=(-k)/(2r)`.
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Knowledge Check

  • A particle of mass m is moving in a horizontal circle of radius R under a centripetal force equal to -A/r^(2) (A = constant). The total energy of the particle is :- (Potential energy at very large distance is zero)

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