Question

A wheel starts from rest and attains an angular velocity of 20 radians/s after being accelerated for 10s. The total angle in radian through which it has turned in 10 s is

• A. $20\pi$
• B. $40\pi$
• C. $100$
• D. $100\pi$

Answer 1

The correct option is C $100$

The inital velocity $=0={\omega }_0$

Final velocity $=20rad/s=\omega$

Total time take $=10s$

$\propto =$ angular acceleration

$=\frac{20-0}{10}=2rad/s^2$

So, $\theta ={\omega }_{0}t+\frac{1}{2}\propto t^2$

$=0+\frac{1}{2}\times 2\times (10{)}^2$

$=100$