MHT CET · Physics · Rotational Motion

A ceiling fan rotates about its own axis with some angular velocity. When the fan is switched off, the angular velocity becomes ${(\frac{1}{4})}^{t h}$ of the original in time $t$ and $n$ revolutions are made in that time. The number of revolution made by the fan during the time interval between switch off and rest are (Angular retardation is uniform)

A $\frac{4 n}{15}$
B $\frac{8 n}{15}$
C $\frac{16 n}{15}$
D $\frac{32 n}{15}$

Verified Solution

Answer & Solution

Correct Answer

(C) $\frac{16 n}{15}$

Step-by-step Solution

Detailed explanation

{(\frac{ω}{4})}^{2} = ω^{2} - 2 α n (2 π)

∴ 2 α n (2 π) = ω^{2} - \frac{ω^{2}}{16}

∴ 2 π n = \frac{15}{16} (\frac{ω^{2}}{2 α})

0 = ω^{2} - 2 α n'

∴ 2 π n^{'} = \frac{ω^{2}}{2 α}

∴ n^{'} = \frac{16}{15} n

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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