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 = $k^{2}r{t}^2$ 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 tha tangetial 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 $v^2$ = $k^{2}r{t}^2$ or v = krt
Tangential acceleration a = $\frac{dv}{dt}$ = kr
Now force F = m $\times$ a = mkr
So power P = F $\times$ v = mkr $\times$ krt = m $k^2{r}^2{t}^2$