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

• A. zero
• B. $m{k}^2{r}^2{t}^2$
• C. $m{k}^2{r}^{2}t$
• D. $m{k}^{2}rt$

Answer 1

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

$a_c=\frac{v^2}{r}=k^{2}r{t}^2\therefore v^2=k^2{r}^2{t}^2$
$\Rightarrow KE=\frac{1}{2}m{v}^2=\frac{1}{2}m{k}^2{r}^2{t}^2$
Using work - energy theorem.
$W=\Delta K=\frac{1}{2}m{k}^2{r}^2{t}^2-0$
$\therefore P=\frac{\Delta K}{\Delta t}=m{k}^2{r}^{2}t$
Hence, the correct answer is option (c).