A wheel rotates 3.5 times in one second. What time (in seconds) does the wheel take to rotate 55 radian of angle ?

Options

A. 1.5
B. 2.5
C. 3.5
D. 4.5

Answer

To solve the problem, we need to find out how long it takes for a wheel that rotates 3.5 times in one second to rotate an angle of 55 radians.

### Step-by-Step Solution:

1. **Determine the angle covered in one rotation**:
- One complete rotation of a wheel corresponds to an angle of \(2\pi\) radians.
- Therefore, in 3.5 rotations, the angle covered is:
\[ \text{Angle in radians} = 3.5 \times 2\pi = 7\pi \text{ radians} \]

2. **Calculate the angle covered in one second**:
- Since the wheel rotates 3.5 times in one second, we can conclude that in one second, the wheel covers an angle of \(7\pi\) radians.

3. **Convert \(7\pi\) to a numerical value**:
- Using the approximation \(\pi \approx \frac{22}{7}\), we can calculate:
\[ 7\pi \approx 7 \times \frac{22}{7} = 22 \text{ radians} \]

4. **Find the time taken to rotate 55 radians**:
- Now, we need to find out how long it takes to rotate 55 radians. We can set up a proportion:
\[ \text{Time} = \frac{\text{Angle to rotate}}{\text{Angle covered in one second}} = \frac{55 \text{ radians}}{22 \text{ radians/second}} \]
- Calculating this gives:
\[ \text{Time} = \frac{55}{22} = 2.5 \text{ seconds} \]

### Final Answer:
The wheel takes **2.5 seconds** to rotate 55 radians.

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