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+1 vote
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in Physics by (50.3k points)
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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 as ac = k2rt2, where k is a constant. The power delivered to the particle by the forces acting on it is

(a) 2πmk2r2

(b) mk2r2

(c) 1/3 mk4r2t5 

(d) 0

1 Answer

+3 votes
by (51.2k points)
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Best answer

Correct Answer is: (b) mk2r2

ac = k 2rt 2 = v 2/r or v = krt.

The tangential acceleration is at = dv / dt = kr.

∴ the net tangential force on the particle = mat = mkr = Ft.

Work is done on the particle only by tangential forces, as the radial forces are perpendicular to v. 

∴ the power delivered to the particle = Ftv = (mkr)(krt) = mk 2r 2t.

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