The length of the seconds hand of laboratory clock is 0.1m. Calculate the speed at the top of the seconds hand

Analysis

To calculate the speed of the tip of the seconds hand, we need to treat the motion as circular motion. The seconds hand moves in a circle, and we are given the radius ($r$) and the time it takes to complete one full revolution (the period, $T$).

Concept

The speed ($v$) of an object moving in a circle is given by the formula:

Where:

• $r$ = radius (length of the seconds hand) = $0.1 \, \text{m}$
• $T$ = period (time taken for the seconds hand to complete one full rotation) = $60 \, \text{seconds}$
• $\pi$ $\approx 3.142$

Solution

1. Identify the variables: • $r = 0.1 \, \text{m}$ • $T = 60 \, \text{s}$

2. Apply the formula: $$v = \frac{2 \times 3.142 \times 0.1}{60}$$

3. Calculate the numerator: $$2 \times 3.142 \times 0.1 = 0.6284$$

4. Divide by the period: $$v = \frac{0.6284}{60}$$ $$v \approx 0.010473 \, \text{ms}^{-1}$$

5. Convert to standard form: $$0.010473 \approx 1.05 \times 10^{-2} \, \text{ms}^{-1}$$

Conclusion

Comparing our result with the given options, we can see that our calculation matches option A.

Exam Tip

When dealing with clock problems in physics, always remember that the period ($T$) depends on the hand in question:

• Seconds hand: $T = 60 \, \text{s}$
• Minute hand: $T = 60 \, \text{minutes} = 3600 \, \text{s}$
• Hour hand: $T = 12 \, \text{hours} = 12 \times 3600 \, \text{s}$