Question

A car wheel is rotated to uniform angular acceleration about its axis. Initially its angular velocity is zero. It rotates through an angle ${\theta }_1$ in the first $2$s. In the next $2$ s, it rotates through an additional angle ${\theta }_2$, the ratio of $\frac{{\theta }_2}{{\theta }_1}$ is

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is C 3

Angular acceleration $\alpha$ = constant
$\Rightarrow \theta =\frac{1}{2}\alpha t^2$

$\Rightarrow {\theta }_1=\frac{1}{2}\alpha (2{)}^2$

$\Rightarrow {\theta }_2+{\theta }_1=\frac{1}{2}\alpha (4{)}^2$

$\Rightarrow \frac{{\theta }_2}{{\theta }_1}=3$