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. (a) zero
B. (b) `mk^2r^2t^2`
C. (c) `mk^2r^2t`
D. (d) `mk^2rt`

Answer

C

Explanation

`a_c=v^2/r=k^2rt^2` or `v=krt`
`KE=1/2mv^2=1/2mk^2r^2t^2`
By work-energy theorem,
`W=DeltaK=1/2mk^2r^2t^2-0`
`P=(dW)/(dt)=mk^2r^2t`
Alternative method: `a_t=(dv)/(dt)=kr`
Power is given by tangential force only. So,
power=`F_tv=ma_tv=mk^2r^2t`
Power of centripetal force is zero.