A solid body rotates about a fixed axis such that its angular velocity depends on θ as omega=k θ^{

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3-2.Motion in Plane

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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

$\theta=\sqrt{2 k t}$

Solution

(d)

$\omega=\frac{k}{\theta}$

$\frac{d \theta}{d t}=\frac{k}{\theta}$

$\int \theta d \theta=k \int d t$

$\frac{\theta^2}{2}=k t$

$\theta=\sqrt{2 k t}$

Standard 11

Physics

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