Question

A particle of mass m is moving in a circular path of constant radius r such that radial acceleration $a_r=k^2{t}^{2}r$. Find the power delivered to the particle by the forces acting on it.

• A. $2\pi m{k}^2{r}^{2}t$
• B. $m{k}^2{r}^{2}t$
• C. $\frac{1}{3}m{k}^4{r}^2{t}^3$
• D. 0

Answer 1

Answer: (B)

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

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

$v=ktr$

$F=\frac{mdv}{dt}=mkr$ and

Power $P=\overline{F}\cdot \overline{v}$

$P=mkr\left(tkr\right)=m{k}^2{r}^{2}t$