The length of minutes hand in a pendulum clock is 10 cm. The speed of the tip of the hand is

Options

A. `pi/6000 ms^(-1)`
B. `pi/18000 ms^(-1)`
C. `pi/3600 ms^(-1)`
D. `pi/1200 ms^(-1)`

Answer

To find the speed of the tip of the minute hand of a pendulum clock, we can follow these steps:

### Step 1: Understand the problem
The length of the minute hand is given as 10 cm. We need to calculate the speed of the tip of the minute hand.

### Step 2: Convert the length to meters
Since speed is generally expressed in meters per second (m/s), we need to convert the length of the minute hand from centimeters to meters.
- Length of the minute hand (r) = 10 cm = 0.1 m

### Step 3: Determine the time period of the minute hand
The minute hand completes one full revolution in 60 minutes (1 hour).
- Time period (T) = 1 hour = 3600 seconds

### Step 4: Calculate the angular velocity (ω)
The angular velocity (ω) can be calculated using the formula:
\[ \omega = \frac{\text{Angular displacement}}{\text{Time taken}} \]
The angular displacement for one complete revolution is \(2\pi\) radians.
\[ \omega = \frac{2\pi \text{ radians}}{3600 \text{ seconds}} = \frac{\pi}{1800} \text{ radians/second} \]

### Step 5: Calculate the linear speed (v) of the tip of the minute hand
The linear speed (v) can be calculated using the formula:
\[ v = \omega \times r \]
Substituting the values we have:
\[ v = \left(\frac{\pi}{1800} \text{ radians/second}\right) \times (0.1 \text{ m}) = \frac{\pi}{18000} \text{ m/s} \]

### Step 6: Final answer
Thus, the speed of the tip of the minute hand is:
\[ v = \frac{\pi}{18000} \text{ m/s} \]