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

Answer

C

Explanation

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