Question

The ratio of the angular speeds of the hour hand and the minute hand of a clock is

• A. 12:1
• B. 1:6
• C. 1:8
• D. None of these

Answer 1

The correct option is A

12:1

Angular Speed

1. The pace at which an object changes its angles, which we measure in radians, in a given time is called angular speed.

Step 1: Given:

1. An hour hand covers 30 degrees in 60 minutes
2. A minute hand covers 360 degrees in 60 minutes

Step 2: Formula Used:

$Angularspeed,\omega =\frac{Anglecovered}{Timetaken}$

Step 3: Calculating the ratio:

An hour hand covers 30 degrees in 60 minutes

So, the angular speed of the hour hand is,

${\omega }_h=\frac{30°}{60min}$

${\omega }_h=0.5degrees/min$

The angular speed of a minute hand is,

A minute hand covers 360 degrees in 60 minutes

So, the angular speed of a minute hand is,

$$\begin{gathered} {\omega }_h=\frac{360°}{60min} \\ {\omega }_h=6degrees/min \end{gathered}$$

The ratio of angular speed of minute hand to hour hand is,

$$\begin{gathered} {\omega }_m:{\omega }_h=6:0.5 \\ \frac{{\omega }_m}{{\omega }_h}=\frac{6}{0.5} \\ \frac{{\omega }_m}{{\omega }_h}=\frac{12}{1} \\ {\omega }_m:{\omega }_h=12:1 \end{gathered}$$

Hence the correct option is (a) 12:1.