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6. system of particles and rotational motion — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics6. system of particles and rotational motion1 Mark
MCQ
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
    $\theta=\sqrt{k t}$
  • ✓
    $\theta=\sqrt{2 k t}$
✓

Answer

Correct option: D.
$\theta=\sqrt{2 k t}$
d
(d)

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

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

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

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

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

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