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Question

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 a = k2rt2 The power delivered to the particle by the forces acting on it is

A
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B
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C
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D
Zero
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Solution

The correct option is B

Here tha tangetial acceleration also exits which requires power.
Given that ac = k2rt2 and ac = v2r v2r = k2rt2
or v2 = k2rt2 or v = krt
Tangential acceleration a = dvdt = kr
Now force F = m × a = mkr
So power P = F × v = mkr × krt = m k2r2t2


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