Question

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

• A. $5$
• B. $1$
• C. $3$
• D. $2$

Answer 1

The correct option is C $3$

Given,
${\omega }_i=0$
For first $2s$
Angular displacement $\theta ={\theta }_1$
For first $4s$
Angular displacement $\theta ={\theta }_1+{\theta }_2$
As we know,
$\theta =\omega t+\frac{1}{2}\alpha t^2$

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

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

From $\left(i\right)$ and $\left(ii\right)$

$\frac{{\theta }_1+{\theta }_2}{{\theta }_1}=4\Rightarrow {\theta }_2=3{\theta }_1\Rightarrow \frac{{\theta }_2}{{\theta }_1}=3$

Final Answer: (c)