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

Rajasthan BoardEnglish MediumSTD 11 SciencePhysics6. system of particles and rotational motion1 Mark
MCQ
When a ceiling fan is switched off, its angular velocity falls to half while it makes $36$ $rotations.$ How many more rotations will it make before coming to rest (Assume uniform angular retardation)
  • A
    $36$
  • B
    $24$
  • C
    $18$
  • ✓
    $12$
✓

Answer

Correct option: D.
$12$
d
$1st \,case:$­­­­­­­

We can write the equation of motion for circular motion as:

$\omega^{2}=\omega_{0}^{2}+2 a \theta_{n}$

Now, $\omega=\frac{\omega_{0}}{2}, \theta=36 \times 2 \pi$ (given)

So, $\frac{\omega_{0}^{2}}{4}=\omega_{o}^{2}+2 \alpha \times 36 \times 2 \pi$

So, $\alpha=\frac{-3 \omega_{0}^{2}}{4 \times 144 \pi}$

$2nd \,case:$

$0=\frac{\omega_{0}^{2}}{4}-2 \times \frac{3 \omega_{0}^{2}}{4 \times 144 \pi} \times \theta$

So, $\theta=24 \pi$ 

So, number of rotations made by the fan before coming to rest

$=\frac{24 \pi}{2 \pi}=12$

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