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 :

Explanation

If v is instantaneous velocity, centripetal
acceleration `a_(c ) = (V^(2))/(r ) rArr (V^(2))/(r ) = k^(2) rt^(2) rArr v =` krt
In circular motion work done by centripetally force is always zero & work is done only by tangential force.
`therefore` Tangent acceleration `a_(r) = (dv)/(dt) = (d)/(dt)` (krt) = kr
`therefore` Tangential force `F_(t) = ma_(t) = `mkr
Power P = `F_(t)v `= (mkr) (krt) = `mk^(2)r^(2)t`