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Question

When a ceilling fan is switched off its angular velocity reduces to $$50\%$$ while it makes $$36$$ rotations. How many more rotation will it make before coming to rest (Assume uniform angular retardation):


A
18
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B
12
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C
36
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D
48
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Solution

The correct option is A $$\;12$$
Let the initial angular velocity of the fan be $$w$$

$$\therefore$$ Its angular velocity when the fan makes 36 rotation       $$w_1  = 0.5w$$

Using        $$w_2^2 - w_1^2  = 2\alpha S$$                 where  $$S = 2\pi (36)  $$ radian

$$\therefore$$    $$(0.5w)^2 - w^2  =2 \alpha \times 2\pi (36)$$            $$\implies 4\pi \alpha  =\dfrac{-0.75w^2}{36}$$

Let the fan makes $$n$$ more rotation before coming to rest.

Using        $$w_3^2 - w_2^2  = 2\alpha S$$                          where  $$S  =2\pi n$$ radian   and   $$w_3 = 0$$

$$\therefore$$    $$0  -(0.5w)^2  = 2 \alpha (2\pi n)$$

OR        $$- 0.25 w^2  = \dfrac{-0.75 w^2}{36} \times n$$                      $$\implies n = 12$$

Physics

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