Question

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

• A. $m^2{K}^2{r}^2{t}^2$
• B. $m{K}^2{r}^{2}t$
• C. $m{K}^{2}r{t}^{2}t$
• D. $mK{r}^{2}t$

Answer 1

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

Since $a_c=k^{2}r{t}^2$

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

$v^2=k^{2}r2t^2$

$v=krt$

$F=m\frac{dv}{dt}=mkr$

$Power=F\times v$

$=\left(mkr\right)\times \left(krt\right)$

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