Question

The tips of the blades in a food blender are moving with a speed of 20m/s in a circle that has a radius of 0.06m. How much time does it take for the blades to make one revolution? (in seconds)
(A) 0.019
(B) 0.2
(C) 0.3
(D) 0.6

Answer 1

Hint:The time taken to complete any path is generally described as distance travelled divided by the velocity (time=distance/velocity). Here the velocity given is the linear velocity along the circumference of the circle of radius 0.6m. So, the distance will be the circumference and the speed is already given.Hence,we can easily calculate it.

Complete step by step answer:
The time taken to complete one revolution is the circumference divided by the linear speed along the circumference given, so,
\[t = \dfrac{{2\pi r}}{v}\]
Here, the radius of the circle is 0.6 m and the velocity is 20 m/s. Hence, substituting the values in the above equation, we get,
\[
t = \dfrac{{2\pi (0.6)}}{{20}}\sec \\
t = 0.019\sec \\
\]
Therefore, the time taken by the blades to make one revolution is 0.019 sec.
The correct answer is option A.
Additional Information:
The angular velocity is given by $\overrightarrow v = \overrightarrow r \times \overrightarrow \omega $, where $\overrightarrow \omega $is the angular velocity. If in the question, the speed was given in terms of angular speed then $\omega = \dfrac{v}{r}$ and time taken $t = \dfrac{{2\pi }}{\omega }\sec $.

Note: Please be careful in substituting the correct formula for time as the speed given is the linear speed along the circumference (meter/second) and not the angular speed $\omega$ (radian/sec).