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 :

Options

A. zero
B. `mk^(2)r^(2)t^(2)`
C. `mk^(2)r^(2)t`
D. `mk^(2)rt`

Answer

`(3)`

Explanation

`a_(c) = v^(2)/r = k^(2)rt^(2) or v = krt`
tangential acceleration is `a_(t) = (dv)/(dt) = kr `hence `therefore P = F_(t) v cos theta = ma_(t) v cos theta`