Question

A fly wheel is revolving at the rate of $300rpm$ on applying a retarding torque, it slows down at the rate of $4rad/s^2$, the time in which it comes to rest is

• A. $5\pi$ $s$
• B. $2.5\pi$ $s$
• C. $1.25\pi$ $s$
• D. $4\pi$ $s$

Answer 1

The correct option is B $2.5\pi$ $s$

$\begin{array}{cc}\text{Given -}& \ast \text{Angular velocity}{w}_0=300\text{rupm}\\ & w_0=600\pi \text{radians}/min=10\pi \text{rad}16.\\ & \ast \text{Angular acceleration}\alpha =4\text{rad}/8^2\end{array}$

$\begin{array}{c}\text{From equation of motion of circular motion -}\\ \begin{array}{c}{\omega }_f={\omega }_0+\alpha t{w}_f\to \text{final angular velocity}\\ 0=10\pi -4\cdot t\\ \Rightarrow t=\frac{10\pi }{4}s=2.5\pi \text{sec}\end{array}\\ \text{Hence, option (B) is correct.}\end{array}$