A particle of mass in is moving in a circular with of constant radius `r` such that its contripetal accelenation `a_(c) ` is varying with time `t` as `a_(c) = K^(2) rt^(2)` where K` is a constant . The power delivered to the particles by the force action on it is

Options

A. `2 pi mk^(2)r^(2)t`
B. `mk^(2)r^(2)t`
C. `1/3 mk^(4)r^(2)t^(5)`
D. 0

Answer

B

Explanation

`P=F_(1).V=ma_(t)V, a_(t)=(d|v|)/dt,v^(2)/r=k^(2)rt^2`
`V=krt rArr P=mxxkrxxkrt`