Question

A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration (a) is varying with time t as a = k 2 rt 2, where k is a constant. The power delivered to the particle by the force acting on it is given as

• A. Zero
• B. mk 2 r 2 t 2
• C. mk 2 r 2 t
• D. mk 2 rt

Answer 1

Answer: (C)

mk 2 r 2 t

Answer 2

The correct answer is (C) : mk 2 r 2 t
$a_r = k²rt² = \frac{v²}{r}$
$⇒ v² = k²r²t²$ or $v = krt$
and
$\frac{d |v|}{dt} = kr$
$⇒ a_t = kr$
$⇒ | \stackrel{→}{F} . \stackrel{→}{v} | = (mkr) ( krt)$
$= mk^2r^2t$= power delivered