The length of a pendulum is 8 m while the pendulum swings through 1.5 rad, find the length of the arc through which the tip of the pendulum passes :

Options

A. 8 m
B. 9 m
C. 12 m
D. none of these

Answer

To find the length of the arc through which the tip of the pendulum passes, we can use the formula for the length of an arc in a circle:

\[ L = r \cdot \theta \]

where:
- \( L \) is the length of the arc,
- \( r \) is the radius (or length of the pendulum), and
- \( \theta \) is the angle in radians.

### Step-by-Step Solution:

1. **Identify the values**:
- The length of the pendulum (radius) \( r = 8 \) m.
- The angle \( \theta = 1.5 \) rad.

2. **Substitute the values into the formula**:
\[ L = r \cdot \theta = 8 \, \text{m} \cdot 1.5 \, \text{rad} \]

3. **Perform the multiplication**:
\[ L = 8 \cdot 1.5 = 12 \, \text{m} \]

4. **Conclusion**:
The length of the arc through which the tip of the pendulum passes is \( 12 \) meters.