Question

A wheel initially at rest, is 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 ${\theta }_2/{\theta }_1$ is:

• A. $4$
• B. $2$
• C. $3$
• D. $1$

Answer 1

Answer: (C)

$3$

Angle revolved in 1 sec and 2 sec are ${\theta }_1$ and ${\theta }_1+{\theta }_2$ respectively.

Given: $w_1=0$ using $\theta =\frac{1}{2}\alpha t^2$

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

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

Solving we get, ${\theta }_2=\frac{3}{2}\alpha$

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