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A particle of mass m is moving in a circ...

A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration `a_(c)` is varying with time t as `a_(c) = k^(2)rt^(2)`, where k is a constant. The power delivered to the particle by the forces acting on it is :

A

` 2 pi m k ^(2) r^(2) t`

B

` m k ^(2) r^(2) t`

C

`( m k ^(4) r^(2) t^(5))/( 3)`

D

Zero

Text Solution

Verified by Experts

The correct Answer is:
B
`a_(c) = k^(2) rt^(2)`
Here `a_(t) ` also exists which requires power
`a_(c) = (v^(2))/(r) = k^(2) rt^(2) rArr v = k r t`
`a_(t) = (dV)/(dt) = kr`
Force (F) = ma = mkr
Power (P) = force ` xx` Velocity `= mkr xx k rt = mk^(2) r^(2) t `
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