  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  B
12  C
36  D
48  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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