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Question

A particle of mass m starts moving in a circular path A of constant radius r in such a way that its centripetal acceleration ac is changing with time as ac=k2r2t2 where k is a constant. What is the power delivered to the particle by the force acting on it?

A
mk2r4t2
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B
mk2r2t2
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C
mk2r3t
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D
mkr4t2
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Solution

The correct option is C mk2r3t
As the particle starts from rest so initial kinetic energy is zero.
Given,
Centripetal acceleration, ac=k2r2t2
We know that, centripetal acceleration is given by, ac=v2r
So, v2r=k2r2t2
v2=k2r3t2
Now, Kinetic energy, K=12mv2
=12mk2r3t2
Power delivered,
P=dKdt=ddt(12mk2r3t2)
=mk2r3t
Hence option (c) is correct.

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