A particle of mass `m` is moving in a circular path of constant radius `r`, such that its centripetal force `F_r` varies with time `t` as `F_r=K^2rt^2`, where k is a constant. What is the power delivered to the particle by the forces acting on it?

Options

A. (a) `2pimk^2r^2t`
B. (b) `mk^2r^2t`
C. (c) `((mk^4r^2t5))/(3)`
D. (d) zero

Answer

B

Explanation

The centripetal acceleration, `a_c=k^2rt^2`
`impliesv^2/r=k^2rt`
`=1/2mv^2=m/2k^2r^2t^2`
`impliesKE =m/2k^2r^2t^2`
`implies (d)/(dt)(KE)=mk^2r^2t^2`
`implies Power =mk^2r^2t`
Alternative method:
Since `v=krt` and tangential acceleration `a_t=(dv)/(dt)=kr`
Tangential force `=mkr`
Instantaneous power, `P=Fxxv=mkrxxkrt=mk^2r^2t`