Question

The angular speed of seconds needle in a mechanical watch is
A. \[\dfrac{\pi }{{30}}\;{\rm{rad/s}}\\ \]
B. \[2\pi \;{\rm{rad/s}}\\ \]
C. \[\pi \;{\rm{rad/s}}\\ \]
D. \[\dfrac{{60}}{\pi }\;{\rm{rad/s}}\]

Answer 1

Hint:
The above problem can be resolved by using the concepts and fundamentals of the mechanical watch. The mechanical watches are used to determine the time. Along with this, the mathematical expression for the angular speed can be used to solve the given problem. In which the time period as a variable is used, and its value for the second's needle is approximately one minute or 60 seconds. The second's needle is the part of a mechanical watch that determines the time is seconds and is utilised to maintain the mechanical stability of the reading.

Complete step by step solution :
The mathematical expression for the angular speed of seconds needle in a mechanical watch is,
\[\omega = \dfrac{{2\pi }}{T}\]
Here, T is the time period in seconds and its value for the second needle is 60 seconds.
Solve by substituting the values in above equation as,
\[\begin{array}{l}
\Rightarrow \omega = \dfrac{{2\pi }}{T}\\
\Rightarrow \omega = \dfrac{{2\pi }}{{\left( {60\;{\rm{s}}} \right)}}\\
\Rightarrow \omega = \dfrac{\pi }{{30}}\;{\rm{rad/s}}
\end{array}\]
Therefore, the magnitude of angular speed for the seconds needle of the mechanical watch is \[\dfrac{\pi }{{30}}\;{\rm{rad/s}}\] and option (A) is correct.

Note:
To solve the given problem, one must be aware of the fundamentals involved in the angular speed and the major terms mentioned in the expression for the angular speed. The concept of angular speed has its applications in designing the mechanical watches and clocks, the mechanical watch and clocks have a wider range of use in showrooms, rooms and conference halls. Moreover, the concept of Time period for the second needle is also required to be taken into consideration, while resolving these problems.