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. ` 2 pi mK^(2)r^(2)t`
B. `mK^(2)r^(2)t`
C. `((mK^(4)r^(2)t^(3)))/(3)`
D. `zero`

Answer

B

Explanation

(b) The constripetal acceleation
` a_(2) = k^(2) r t^(2) rArr (V^(2)/(r) = K^(2) r t^(2) `
`rArr (1)/(2) mv^(2) = (m)/(2) K^(2) r^(2)t^(2)` ....(i)
`rArr K.E = (m)/(2) K^(2) r^(2)t^(2) rArr (d)/(dt) (K.E ) = mk^(2)r^(2)t^(2)`
`rArr power = mk^(2)r^(2) t^(2) `