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IF a particle of mass m is moving i...

IF a particle of mass m is moving in a horizontal circle of radius r with a centripetal force `(-(K)/(r^(2)))` , then its total energy is

A

`-beta//2R`

B

`betaxx2R`

C

`-(2beta)/ (R )`

D

`(2 R)/( beta)`

Text Solution

Verified by Experts

The correct Answer is:
A
Given, centripetal force `(F) = (beta)/(R^2)`
`therefore` Potential energy `=U= int_(oo)^(R ) F. dR = beta int_(oo)^( R) (dR)/( R^2)`
`rArr U= beta [-(1)/( R) ]_(oo)^(R ) rArr U= (-beta)/( R)`
`therefore` Kinetic energy `=(1)/(2) mv^(2) = (R)/ (2) ((mv^(2))/( R))= (R)/( 2). (beta)/(R^2)`
`rArr K.E. = (beta)/(2R)`
Total energy `=K.E. + P.E. = (beta)/( 2R) - (beta)/( R) = - (beta)/( 2R)`
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