Question

The two wheels are couples with a belt. The ratio of the angular velocities of $A$ and $B$ is when the ratio of radii is 1:3 respectively

• A. $3:2$
• B. $1:3$
• C. $3:1$
• D. $9:1$

Answer 1

The correct option is C $3:1$

$\begin{array}{c}\text{Since the two wheels are coupled with same}\\ \text{belt henu the velocity of every point on the}\\ \text{belt will be equal.}\\ \text{Of wheel of small radius equals to}\\ \text{the Doint on the wheel of larger readius}\\ \Rightarrow w_1{\mu }_1=w_2{\mu }_2\\ \Rightarrow \frac{{\omega }_1}{{\omega }_2}=\frac{r_2}{{\mu }_1}=\frac{3}{1}\Rightarrow \frac{w_1}{{\omega }_2}=\frac{3}{T}=3:1\\ \text{Hence, option (D) is correct.}\end{array}$