Question

A wheel initially at rest, is now rotated with a uniform angular acceleration. The wheel rotates through an angle ${\theta }_1$ in first one second and through an additional angle ${\theta }_2$ in the next one second. The ratio $\frac{{\theta }_2}{{\theta }_1}$ is

• A. 4
• B. 2
• C. 3
• D. 1

Answer 1

The correct option is C 3

Angular displacement in first one second ${\theta }_1=\frac{1}{2}\alpha (1{)}^2=\frac{\alpha }{2}...(i)$ $[From\theta ={\omega }_{1}t+\frac{1}{2}\alpha t^2]$
Now again we will consider motion from the rest and angular displacement in total two seconds
${\theta }_1+{\theta }_2=\frac{1}{2}\alpha (2{)}^2=2\alpha ...(ii)$
Solving (i) and (ii) we get ${\theta }_1=\frac{1}{2}$ and ${\theta }_2=\frac{3\alpha }{2}$ $\therefore \frac{{\theta }_2}{{\theta }_1}=3.$