Question

The second’s hand of a clock is $10cm$ long. It goes round once every $60seconds$.
(a) What is the average speed of the tip of the second hand?
(b) What is the distance travelled by the tip in $10seconds$?
(c) What is its average velocity during the time it makes one revolution? (Take $\mathrm{\pi }=3.14$)

Answer 1

(a)

Step 1: Given data

Length of second's hand = $10cm$

It complete one revolution in $60seconds$

Step 2: Calculating the distance covered by second's hand

Here, the distance will be the circumference of the circle that second-hand makes in one complete revolution.

Therefore, $dis\tan ce=2\times \mathrm{\pi }\times \mathrm{r}\left(\mathrm{circumference}\right)$
radius, $r=10cm(lengthofsecondhand)$
$dis\tan ce=2\times 3.14\times 10cm$
$dis\tan ce=62.8cm$

Step 3: Formula used to calculate the speed

we know that, $speed=\frac{dis\tan ce}{time}$

Step 4: Calculating speed of the tip
Now, the time it takes to complete one full revolution by second hand = $60seconds$
$speed=\frac{62.8cm}{60seconds}$
$speed=1.0466cm/second$

Therefore, speed of the tip of $10cm$ long second hand of a clock is $1.0466cm/second.$.

(b)

Step 5: Distance travelled by the tip in 10 seconds
We have $speed=1.0466cm/sec$
$Timetaken=10s$
So, distance travelled = $speed\times time=1.0466\times 10=10.466cm$
Thus ,distance travelled by the tip in $10seconds$ is $10.466cm$.

(c)

Step 6: Average velocity during the time it makes one revolution
$Averagevelocity=\frac{displacement}{time}$
Displacement =$0cm$ (as hand of clock completes one complete revolution, therefore, initial position of hand and final position of the hand are same)
Time = $60s.$
$Averagevelocity=\frac{displacement}{time}=\frac{0}{60}=0m/s.$

Hence, the average velocity during the time it makes one revolution is $0m/s.$