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The time rate of change of energy

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What is the power given by centripetal force?(in circular motion)

The power given to the particle by the force acting on it is? MY ATTEMPT: Since force and velocity are radial power must be zero, but the answer is not zero . … If I find instantaneous power then I am getting $P_i = 2 \pi m k^2 r^2 t$. Where $P_i$ = instantaneous power, The answer given is option (b), as in the following figure, but why? …
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