Question

A clock has a minute hand of length 14 cm. At what speed does the tip of the minute hand move in a duration of half an hour?

• A. $\frac{7}{450}$$cm{s}^{-1}$
• B. $\frac{11}{450}cm{s}^{-1}$
• C. $\frac{44}{450}$$cm{s}^{-1}$
• D. $\frac{16}{750}$$cm{s}^{-1}$

Answer 1

The correct option is B

$\frac{11}{450}cm{s}^{-1}$

Step 1: Given Data

1. The length of the minute hand of a clock is 14 cm.
2. The minute hand moves for a time period of half an hour.So time t = 30 min = $30\times 60$ second = $1800$s.

Step 2: Calculation of speed of the minute hand

1. The length of the minute hand of the clock acts as the radius for the circular path of the clock. So r = 14 cm.
2. We know that the minute hand completes one full circle in one hour. So for half an hour, the minute hand will cover only the half-circle.
3. So the distance covered by the minute hand will be,
4. Distance= $\frac{circumference}{2}$= $\frac{2\mathrm{\pi r}}{2}$=$\frac{2\times 22\times 14}{7\times 2}$= $44$cm.
5. Now the speed of the minute hand will be,
6. Speed= $\frac{dis\tan ce}{time}$= $\frac{44}{1800}$$cm{s}^{-1}$=$\frac{11}{450}$$cm{s}^{-1}$.

Hence,

The speed of a minute hand is$\frac{11}{450}$$cm{s}^{-1}$