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  4. A particle of mass m moves in a circular path of radius r, under the action of force which delivers it constant power p and increases its speed. The angular acceleration of particle at time (t) is proportional

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Q. A particle of mass $m$ moves in a circular path of radius $r$, under the action of force which delivers it constant power $p$ and increases its speed. The angular acceleration of particle at time $(t)$ is proportional

Work, Energy and Power

Solution:

Work $=P t$
Using $W=\Delta K$
$P t=\frac{1}{2} m(r w)^{2}$
$P t=\frac{1}{2} m r^{2} w^{2}$
$P t=\frac{1}{2} m r^{2} \alpha^{2} t^{2}$
$\left(\because \alpha=\frac{w}{t}\right)$
So $\alpha^{2} \propto \frac{1}{t}$
$\Rightarrow \alpha \propto \frac{1}{\sqrt{t}}$