Question

The ratio of angular speed of minute hand to that of hour hand of a watch is:
A) $6:1$
B) $1:6$
C) $1:12$
D) $12:1$

Answer 1

In order to solve this question, the concept of changing the distance covered by an hour and minute hand of the clock into degrees is very important. The focus should be on the units of angular speed. In ratio the final units are cancelled so the units of angular speed of both minute hand and hour hand should be the same. The concept and formula of angular velocity is also important here.

Complete step by step answer:
Here we have to find the ratio of angular speed of minute and hour hand.
So, let us first find the angular speed of minute and hour hand respectively.
The hour hand of a clock covers $30$ degrees in $60$ minutes.
So, the angular speed of the hour hand would be given by,
${\omega _h} = \dfrac{{30°}}{{60 \text{minutes}}}$
On simplification we get,
${\omega _h} = 0.5\deg /\min$
Now the angular speed of minute hand is given by,
A minute hand covers $360$ degrees in $60$ minutes,
So, we have the angular speed of minute hand as,
${\omega _m} = \dfrac{{360°}}{{60 \text{minutes}}}$
On simplification we get,
${\omega _m} = 6\deg /\min$
Now the ratio of angular speed of minute hand to hour hand would be given as,
${\omega _m}:{\omega _h} = 6:0.5$
As, $0.5 = \dfrac{1}{2}$
So, on simplification we have,
${\omega _m}:{\omega _h} = 12:1$

So, the correct answer is option C, ${\omega _m}:{\omega _h} = 12:1$.

Note: It is important to note that $360$ degrees make a complete circle. Here, the minute hand covers the whole complete circle in $60$ minutes but the hour hand covers just $30$ degrees in $60$ minutes. This creates a huge difference in the angular speed of the minute hand and hour hand of a clock. This concept helped us in calculating the answer properly.