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 the time `t` as
`a_(c)=k^(2)r^(3)t^(4)`
where `k` is a constant. The power delivered to the particle by the forces acting on it is

Options

A. `1/3mk^(2)r^(4)t^(5)`
B. `mk^(2)r^(2)t`
C. `2mk^(2)r^(4)t^(3)`
D. zero

Answer

C

Explanation

Centripetal acceleration
`a_(c)=K^(2)r^(3)t^(4)`
`:.(v^(2))/r=k^(2)r^(3)t^(4)`
`impliesv^(2)=k^(2)r^(4)t^(4)`
or `v=kr^(2)t^(2)`
Tangential acceleration `a_(t)=(dv)/(dt)`
`d/(dt)(kr^(2)t^(2))=2kr^(2)t`
In circular motion no power is delivered by centripetal force `( :' F_|_v)`
`:.` Power delivered by tangential force
`P=F_(t)v=ma_(t)v=m2kr^(2)t.kr^(2)t^(2)`
`=2mk^(2)r^(4)t^(3)`