Question: A table clock has its minute hand 9 cm long. What is the average velocity of the tip of the minute h...

Question

A table clock has its minute hand 9 cm long. What is the average velocity of the tip of the minute hand (a) between 3 am to 3:30 am and (b) between 3 am to 3 pm?

Answer 1

Solution

To solve this question, we will make use of the formula of velocity. We will convert the time from minutes to seconds. Then we will find the displacement of the minute hand by calculate the number of revolutions taking place.

Complete step by step answer:
We know that velocity is the ratio of displacement of a body and the time in which it takes place. So, $v = \dfrac{d}{t}$
(a) On converting the length of the minute hand from centimetre to metre, we get,
$9cm = 0.09m$
Similarly, on converting 30 minutes between 3 am to 3:30 am into seconds, we get,
$30\,minutes = 30 \times 60\,s$
$\Rightarrow 30\,minutes = 1800\,s$

From 3 am to 3:30 am, the minute hand makes half revolution, but the displacement of the tip is double the length of the minute hand.So,
$d = 2 \times 0.09$
$\Rightarrow d = 0.18\,m$
$\Rightarrow v = \dfrac{{0.18}}{{1800}}\,\dfrac{m}{s}$
On further solving this, we get,
$\therefore v = 0.0001\,\dfrac{m}{s}$

(b) Similarly, from 3 am to 3 pm, the minute hand makes 12 revolutions but the displacement in this case is zero as from where the minute hand started, it finished there only. Since the displacement is zero, so the velocity will also be zero as velocity is the ratio of displacement and time.
$v = 0\dfrac{m}{s}$
So, the average velocity of the tip of the minute hand between 3 am to 3:30 am is $v = 0.0001\dfrac{m}{s}$ and the average velocity of the tip of the minute hand between 3 am to 3 pm is $v = 0\dfrac{m}{s}$ .

Note: It is important to note that in this question we have to calculate the average velocity. So, we need to find the displacement and not the distance. So, in the last case the average velocity is zero because the displacement is zero. If in the question, it would have been asked to calculate the average speed, then the value of average speed would not have been zero as some distance has been travelled by the minute hand of the clock.