Question

A constant power is supplied to a disc that can rotate freely about a fixed vertical axis. Angular velocity ($\omega$)of the disc varies with the number of rotations ($n$) made by the disc after starting from rest as $\omega =h{n}^{1/x}$ then $x$ is : ($K$ is constant)

Answer 1

$\tau =I\alpha$
$P=\tau \omega$
$P=I\alpha \times \omega$
$P=I{\omega }^2\frac{d\omega }{d\theta }$
${\omega }^{2}d\omega \alpha d\theta \Rightarrow \frac{{\omega }^3}{3}\alpha \theta$
$\omega \times {\theta }^{1/3}$