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. $48$

Answer 1

Answer: (B)

$12$

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 $S=2\pi \left(36\right)$ radian

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

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 $-0.25w^2=\frac{-0.75w^2}{36}\times n$ $⟹n=12$