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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) 2πmk2r2t (b) mk2r2t (c) 1/3 mk4r2t5 (d) 0 |
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Answer» Correct Answer is: (b) mk2r2t 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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