Question

A particle of mass in is moving in' a circular path of constant radius $r$ such that its centripetal acceleration is varying with time $t$ as $a_c=k^{2}r{t}^2$, where $k$ is the constant. The power delivered to the particle by the forces acting on it is

• A. $2\pi m{k}^2{r}^2$
• B. $m{k}^2{r}^{2}t$
• C. $\frac{\left(m{k}^4{r}^2{t}^5\right)}{3}$
• D. Zero

Answer 1

Answer: (B)

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

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

kinetic energy $E=\frac{1}{2}m{v}^2=\frac{m{r}^2{k}^2{t}^2}{2}$

power$=\frac{dE}{dt}=\frac{2m^2{k}^{2}t}{2}=m{r}^2{k}^{2}t$