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JEE Main 2022 (28 Jun, Shift 1) · Non-Uniform Circular Motion

Non-Uniform Circular Motion question from JEE Main 2022 (28 Jun, Shift 1)

Q15JEE Main 2022 · 28 JUN · SHIFT 1Difficult

Non-Uniform Circular Motion

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

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Answer: (c)

$a_c = \frac{v^2}{r} = k^2 r t^2 \Rightarrow v = krt$
Tangential acceleration: $a_t = \frac{dv}{dt} = kr$
Only the tangential force does work: $P = m a_t v = m(kr)(krt) = mk^2r^2t$
So the answer is (c).

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