When a pendulum of length 50 cm oscillates, it produces an arc of 16 cm The angle so formed in degree measure is (approx.)

Options

A. `18^@25`
B. `18^@35'`
C. `18^@20`
D. `18^@08`

Answer

To find the angle formed by a pendulum of length 50 cm that produces an arc of 16 cm, we can use the formula for the arc length of a circle:

\[ \text{Arc Length} = r \cdot \theta \]

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

However, since we want the angle in degrees, we can adjust the formula to:

\[ \text{Arc Length} = \frac{r \cdot \theta \cdot \pi}{180} \]

Given:
- Length of the pendulum \( r = 50 \) cm,
- Arc length \( = 16 \) cm.

We can rearrange the formula to solve for \( \theta \):

\[ \theta = \frac{\text{Arc Length} \cdot 180}{r \cdot \pi} \]

Now, substituting the values:

\[ \theta = \frac{16 \cdot 180}{50 \cdot \pi} \]

Calculating the values step-by-step:

1. Calculate \( 16 \cdot 180 \):
\[ 16 \cdot 180 = 2880 \]

2. Calculate \( 50 \cdot \pi \):
\[ 50 \cdot \pi \approx 50 \cdot 3.14 = 157 \]

3. Now substitute these values back into the equation for \( \theta \):
\[ \theta = \frac{2880}{157} \]

4. Performing the division:
\[ \theta \approx 18.3 \text{ degrees} \]

Thus, the angle formed is approximately \( 18.3 \) degrees.