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A particle of mass m moves on a circular...

A particle of mass m moves on a circular path of radius r . Its centripetal acceleration is `kt^(2)` , where k is a constant and t is time . Express power as function of t .

A

kmt

B

ktmr

C

km/t

D

kmr/t

Text Solution

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The correct Answer is:
B
Here radial centripetal acceleration `a = (v^(2))/r `
` = kt^(2) ` is given
Now , taking derivation w.r.t time , t .
`(2v (dv)/(dt)) 1/r = 2 kt`
Multiplying on both sides by .m.
` :. Mv (dv)/(dt) = mktr`
` :. Fv = ktmr " " ( :. F = ma = m (dv)/(dt))`
` :. P = ktmr " " ( :. P = Fv)`
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