The particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration `a_(c)` is varying with time t as `a_(c)` = `k^(2)` , Where k is a constant .The power delivered to particle by the forces actingon it is

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`