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Question

A particle of mass m is moving in a horizontal circle of radius r, under a centripetal force equal to (kr2) where k is constant. What is the total energy of the particle?

A
-K2r
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B
-K2r2
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C
K22r
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D
-Kr
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Solution

The correct option is A -K2r

As centripetal force is mv2r hence mv2r = kr2

K.E. of particle = mv2 = K2r.

The force acting on a particle is conservative in nature hence we can find potential energy of the particle as

F = -dvdt dv = -Fdr

U = rFdr rKr2 dr

U = -Kr

Total energy of particle = K.E. + P.E. = -Kr + K2r= -K2r.


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