Question
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 r t^2`. The power is
Answer: Option B
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`a_c = v^2/r = k^2 r t^2`
`because v = krt`
The tangential accelerationis
`a_1 = (dv)/(dt) = (d(rt))/(dt) = kr`
The work done by centripetal force will be zero.
so , power is delivered to the particle by only tangential force which acts in he same direction of instantaneous velocity .
`:.` power = `F_1 v`
= `ma_1 krt`
= `m(kr) (krt) = mk^2 r^2 t`
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