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

• A.
• B.
• C.
• D. Zero

Answer 1

The correct option is B

Here the tangential acceleration also exits which requires power.

Given that $a_c=k^{2}r{t}^2$ and $a_c$ = $\frac{v^2}{r}$

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

or $v^2$ = $k^2{r}^2{t}^2$ or $v$ = $krt$

Tangential acceleration $a$ = $\frac{dv}{dt}$ = $kr$

Now force $F=m\times a=mkr$

So power $P=F\times v=mkrkrt=m{k}^2{r}^{2}t$