Question

A wheel starts from the rest and attains an angular velocity of $20\text{rad/s}$ after being uniformly accelerated for $10\text{s}$. The total angle in radians through which it has turned in $10\text{s}$ is

• A. 20
• B. 40
• C. 80
• D. 100

Answer 1

The correct option is D 100

${\omega }_i=0rad/s$, ${\omega }_f=20rad/s$
And
${\omega }_f={\omega }_i+\alpha t$
$20=0+\alpha 10$
$\alpha =2rad/s^2$
Now,
$\begin{array}{cc}\theta & ={\omega }_{i}t+\frac{1}{2}\alpha t^2\\ \theta & =(0\times 10)+\frac{1}{2}\times 2\times 100\\ & =100\end{array}$