A 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)rt^(2)`, where k is a constant. The power delivered to the particle by the forces acting on it is :

Options

A. `m^2K^2r^2t^2`
B. `mK^2r^2t`
C. `mK^2rt^2`
D. `mKr^2t`

Answer

B

Explanation

The centripetal acceleration ,
`a_c =K^2rt^2`
`or" "V^2//r=K^2rt^2`
`or" "v=Krt`
So tangential acceleration ,
`a_t =(dv)/(dt)=Kr `
Power =`F_tvcos0^@=(ma_t)(Krt)`
`(mKr)(Krt)=mL^2r^2t`