A constant power is supplied to a rotating disc. Angular velocity… - Vidyadip

MCQ

A constant power is supplied to a rotating disc. Angular velocity $\left( \omega \right)$ of disc varies with number of rotations $(n)$ made by the disc as

✓
$\omega \propto {\left( n \right)^{1/3}}$
B
$\omega \propto {\left( n \right)^{3/2}}$
C
$\omega \propto {\left( n \right)^{2/3}}$
D
$\omega \propto {\left( n \right)^2}$

✓

Answer

Correct option: A.

$\omega \propto {\left( n \right)^{1/3}}$

a
$P=\tau \cdot \omega$

$P=I \alpha \cdot \omega=I\left(\omega \frac{d \omega}{d \theta}\right) \cdot \omega$

$\omega^{2} \mathrm{d} \omega=\frac{\mathrm{P}}{\mathrm{I}} \mathrm{d} \theta$

$\omega \propto \theta^{1 / 3}$

$\omega \propto(\mathrm{n})^{1 / 3}$

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