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PhysicsW.E.P.PowerEasy2 minPYQ_2020

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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 $a_{c} = k^{2} {r t}^{2}$ , where $k$ is a constant. The power delivered to the particle by the force acting on it is

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Answer:

Solution:

$a_{c} = k^{2} {r t}^{2}$

or $\frac{v^{2}}{r} = k^{2} {r t}^{2}$

or $v = k r t$

Therefore, tangential acceleration, $a_{t} = \frac{d v}{d t} = k r$

or Tangential force,

$F_{t} = {m a}_{t} = m k r$

Only tangential force does work.

$P o w e r = F_{t} v = (m k r) (k r t)$

or $P o w e r = {m k}^{2} r^{2} t$

Stream:JEESubject:PhysicsTopic:W.E.P.Subtopic:Power

⏱ 2mℹ️ Source: PYQ_2020

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