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. `2pimk^(2)r^(2)t`
B. `mk^(2)r^(2)t`
C. `(mk^(4)r^(2)t^(5))/(3)`
D. `zero`

Answer

B

Explanation

`a_(c)=k^(2)et^(2)`
`(v^(2))/(r )=k^(2)rt^(2)impliesv=krt`
`a_(t)=(dv)/(dt)=kr`
`F_(t)=ma_(t)=mkr`
`P=vecF_(t).vecv=F_(t)v=mkrxxkrt=mk^(2)r^(2)t`