Question

A particle of mass $m$ is moving in a circular path of constant radius $r$ such that its centripetal acceleration $a_c$ varies with the 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. $\frac{\left(m{k}^4{r}^2{t}^5\right)}{3}$
• D. $zero$

Answer 1

Answer: (B)

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

$a_c=k^{2}r{t}^2=\frac{v^2}{r}\Rightarrow v^2=k^2{r}^2{t}^2\Rightarrow v=krta=\frac{dv}{dt}=kr$
power $=Fv$

$=mav$

$=m\times kr\times krt$

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