A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration ac is varying with time t as ac=k2 rt2 , where k is a constant. The power delivered to the particle by the force acting on it is

Question

A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration ac is varying with time t as ac=k2 rt2 , where k is a constant. The power delivered to the particle by the force acting on it is (A) 2π mk2r2 (B) mk2 r2t (C) ((m k4 r2 t5)/3) (D) Zero

Tardigrade Admin · Accepted Answer

ac=k2 r t2 or (v2/r)= k2 r t2 or v=krt Therefore, tangential acceleration, at =(d v/d t)= kr or Tangential force, Ft=m at=mkr Only tangential force does work. Power =Ft v=(m k r)(k r t) or Power =m k2 r2 t

Q. 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

$2 π m k^{2} r^{2}$

$m k^{2} r^{2} t$

$\frac{( m k ^{4} r ^{2} t ^{5} )}{3}$

Zero

$a_{c} = k^{2} r t^{2}$
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,
$F_{t} = m a_{t} = mk r$
Only tangential force does work.
Power $= F_{t} v = (mk r) (k r t)$
or Power $= m k^{2} r^{2} t$

Q. A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration ac​ is varying with time t as ac​=k2rt2 , where k is a constant. The power delivered to the particle by the force acting on it is

2πmk2r2

mk2r2t

3(mk4r2t5)​