Question

A particle of mass $m$ is moving in a circular path of constant radius $r$ such that its centripetal accleration $a_c$ is varying with time as $a_c=k^{2}r{t}^2$, where $k$ is a constant. The power delivered to the particle by the forces acting on it is-

• A. $2\pi m{k}^2{r}^{2}t$
• B. $m{k}^2{r}^{2}t$
• C. $\frac{1}{3}m{k}^4{r}^2{t}^5$
• D. $0$

Answer 1

Answer: (B)

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

Centripetal acceleration is $v^2/r=k^{2}r{t}^2\Rightarrow v=krt$

Tangential acceleration is $dv/dt=kr$.

So tangential force is $F_t=mkr$

work done is always due to tangential force. Work done due to centripetal force is zero as centripetal force is perpendicular to the displacement which is along the tangential direction.

So power delivered is $F_{t}v=mkr\times krt=m{k}^2{r}^{2}t$