Question

A solid body rotates about a fixed axis such that its angular velocity depends on $\theta$ as $\omega=k \theta^{-1}$ where $k$ is a positive constants. At $t=0, \theta=0$, then time dependence of $\theta$ is given as

• A. $\theta=k t$
• B. $\theta=2 k t$
• C. $\theta=\sqrt{k t}$
• D. $\theta=\sqrt{2 k t}$

Answer 1

Answer: (D)

$\omega=\frac{k}{\theta}$
$\frac{d \theta}{d t}=\frac{k}{\theta}$
$\int \theta d \theta=k \int d t$
$\frac{\theta^{2}}{2}=k t$
$\theta=\sqrt{2 k t}$