A circular disc is rotating about its own axis at a uniform angular velocity ‘ω ‘. The disc is subjected to uniform angular retardation by which its angular velocity is decreased to ω/2 during 120 rotations. The number of rotations further made by it before coming to rest is

# A circular disc is rotating about its own axis at a uniform angular velocity 'ω '. The disc is subjected to uniform angular retardation by which its angular velocity is decreased to ω/2 during 120 rotations. The number of rotations further made by it before coming to rest is

1. A

120

2. B

60

3. C

40

4. D

20

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### Solution:

as $\alpha$ constant
$\mathrm{\alpha }=\frac{{\mathrm{\omega }}^{2}-{{\mathrm{\omega }}_{0}}^{2}}{2\mathrm{\theta }}=\frac{{\mathrm{\omega }}^{2}-{{\mathrm{\omega }}_{0}}^{2}}{2\left(2\mathrm{\pi N}\right)}$

$\therefore \mathrm{N}\propto {\mathrm{\omega }}^{2}-{{\mathrm{\omega }}_{0}}^{2}$

$\frac{\mathrm{N}}{{\mathrm{N}}^{\text{'}}}=\frac{{\left(\frac{\mathrm{\omega }}{2}\right)}^{2}-{\mathrm{\omega }}^{2}}{0-{\left(\frac{\mathrm{\omega }}{2}\right)}^{2}}=\frac{\frac{-3}{4}}{\frac{-1}{4}}=3$

$\therefore {\mathrm{N}}^{\text{'}}=\frac{\mathrm{N}}{3}=\frac{120}{3}=40$

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