Question

A particle of mass m is moving in a circular path of constant radius r such that is 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 force acting on it is :

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

Answer 1

The correct option is B $m{k}^2{r}^{2}t$

$a_c=k^{2}r{t}^2$
i.e. $\frac{v^2}{r}=k^{2}r{t}^2$ or $v=krt$
Also $a_t=\frac{dv}{dt}=kr$
$\therefore F=m{a}_t=mkr$
Then, $power=\int Fdv=\int (mkr\times kr)dt=m{k}^2{r}^{2}t$