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

• A. $2\pi mk^{2}r^{2}t$
• B. $mk^{2}r^{2}t$
• C. $\frac{mk^{4}r^{2}t^{5}}{3}$
• D. Zero

Answer 1

Answer: (B)

$mk^{2}r^{2}t$

Answer 2

$a_{c} = k^{2}rt^{2}$ $\Rightarrow$ $\frac{v^{2}}{r} = k^{2}rt^{2}$ $\Rightarrow$ $v^{2} = k^{2}r^{2}t^{2}$

⇒ $v = krt$

Tangential acceleration $a_{t} = \frac{dv}{dt} = kr$

As centripetal force does not work in circular motion.

So power delivered by tangential force $P = F_{t}v = ma_{t}v$ =m(kr) krt $= mk^{2}r^{2}t$