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

• A. $2\pi m{k}^2{r}^{2}t$
• 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 $m{k}^2{r}^{2}t$

The centrifugal force $\frac{m{v}^2}{r}$

Centripetal force

$\Rightarrow \frac{m{v}^2}{r}=m.k^2.r{t}^2\Rightarrow V=krt$

Tangential accelration $=\frac{dv}{dt}=kr$

$\therefore$ Power delivered $=Force\times Velocity=mkr\times Krt=m{K}^2{r}^{2}t$