Question

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

• A. 1
• B. 2
• C. 3
• D. 5

Answer 1

The correct option is C 3

Using relation $\theta$ = ${\omega }_0$t + $\frac{1}{2}$ $\alpha$ $t^2$
${\theta }_1$ = $\frac{1}{2}$ ($\alpha$) $2^2$ = 2 $\alpha$ ..(i) (As ${\omega }_0=0,t=2sec$)
Now using same question for t = 4 sec , ${\omega }_0$ = 0
${\theta }_1$ + ${\theta }_2$ = $\frac{1}{2}$ ${\left(4\right)}^2$ = 8 $\alpha$ ..(ii)
From (i) and (ii), ${\theta }_1$ = 2 $\alpha$ and ${\theta }_2$ = 6$\alpha$ $\therefore$ $\frac{{\theta }_1}{{\theta }_2}$ = 3