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Q.

A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration ac is varying with time t as ac=k2rt2,, where k is a constant. The power delivered to the particle by the forces acting on it is

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a

Zero

b

mk2r2t2

c

mk2r2t

d

mk2rt

answer is C.

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Detailed Solution

ac=v2r=k2rt2 or v=krtKE=12mv2=12mk2r2t2By work-energy theorem, W=ΔK=12mk2r2t2−0P=dWdt=mk2r2tAlternative method : at=dvdt=krPower is given by tangential force only. So, power =Ftv=matv =mk2r2tPower of centripetal force is zero.
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A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration ac is varying with time t as ac=k2rt2,, where k is a constant. The power delivered to the particle by the forces acting on it is