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6.System of Particles and Rotational Motion
medium
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
A
$\omega \propto {\left( n \right)^{1/3}}$
B
$\omega \propto {\left( n \right)^{3/2}}$
C
$\omega \propto {\left( n \right)^{2/3}}$
D
$\omega \propto {\left( n \right)^2}$
Solution
$P=\tau \cdot \omega$
$P=I \alpha \cdot \omega=I\left(\omega \frac{d \omega}{d \theta}\right) \cdot \omega$
$\omega^{2} \mathrm{d} \omega=\frac{\mathrm{P}}{\mathrm{I}} \mathrm{d} \theta$
$\omega \propto \theta^{1 / 3}$
$\omega \propto(\mathrm{n})^{1 / 3}$
Standard 11
Physics
