Question

An insect trapped in a circular groove of radius $12cm$ moves along the groove steadily and completes $7$ revolutions in $100sec$. What is the angular speed and linear speed of motion?

• A. $0.11rad/s,3.28cm/s$
• B. $0.40rad/s,5cm/s$
• C. $0.44rad/s,5.28cm/s$
• D. None of these

Answer 1

The correct option is C

$0.44rad/s,5.28cm/s$

Explanation for correct option

Step 1: Given

1. Circular groove of radius = $12cm$
2. Insects completes $7$ revolutions in $100sec$
3. The time period of revolution can be calculated as $T=\frac{100}{7}sec$

Step 2: Formula used

1. Angular Speed $\omega =\frac{2\pi }{T}$ where $T$ is the time period of revolution
2. Linear speed of motion $v=\omega r$ where $\omega$ is the angular speed and $r$ is the radius of the

Step 3: Find the angular speed

The time period of revolution can be calculated as $T=\frac{100}{7}sec$

$$\begin{gathered} \therefore \omega =\frac{2\pi }{T} \\ \Rightarrow \omega =\frac{2\pi }{{\displaystyle \raisebox{1ex}{$100$}\!\left/ \!\raisebox{-1ex}{$7$}\right.}} \\ =0.44rad{s}^{-1} \end{gathered}$$

Step 4: Find the linear speed of the motion

Circular groove of radius = $12cm=0.12m$

$$\begin{gathered} \therefore v=\omega r \\ \Rightarrow v=\left(0.44\right)\left(12\right) \\ =5.28cm{s}^{-1} \end{gathered}$$

Hence option C is correct