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

Answer

B

Explanation

F = ma
Here, a `= K^(2)rt^(2)`
So, `F = mK^(2)rt^(2)`
Power P = F.v
`:. v= r/t`
`:. P = mK^2 t^2 xxr/t = mK^2 r^2 t`