# A wheel has a speed of 1200 revolution per minute and is made to slow down at a rate of $4\;radian/s^2$. The number of revolutions it makes before coming to rest is

$\begin {array} {1 1} (a)\;143 & \quad (b)\;272 \\ (c)\;314 & \quad (d)\;722 \end {array}$

$w^2= w_0^2 - 2 \alpha \theta$
$\theta= \large\frac{w_0^2}{2 \alpha}$
$\qquad= \large\frac{(2 \pi \times 1200 /60 )^2}{2 \times 4}$
$\qquad = \large\frac{4 \pi ^2 \times 400}{2 \times 4}$
$2 \pi n= 2 \pi ^2 \times 100$
$n= \pi \times 100= 314$