A wheel makes 360 revolutions in a minute. The number of radians through which it turns in one second is

Options

A. `12 pi`
B. `11 pi`
C. `10 pi`
D. `8pi`

Answer

To find the number of radians through which a wheel turns in one second, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the number of revolutions per minute**:
The wheel makes 360 revolutions in one minute.

2. **Convert revolutions to radians**:
We know that one complete revolution is equal to \(2\pi\) radians. Therefore, the total radians for 360 revolutions can be calculated as:
\[ \text{Total radians in one minute} = 360 \text{ revolutions} \times 2\pi \text{ radians/revolution} \]
\[ = 720\pi \text{ radians} \]

3. **Convert minutes to seconds**:
Since we need to find the number of radians per second, we convert minutes to seconds. There are 60 seconds in a minute.

4. **Calculate radians per second**:
To find the number of radians turned in one second, we divide the total radians in one minute by the number of seconds in a minute:
\[ \text{Radians per second} = \frac{720\pi \text{ radians}}{60 \text{ seconds}} \]
\[ = 12\pi \text{ radians/second} \]

5. **Conclusion**:
Thus, the number of radians through which the wheel turns in one second is \(12\pi\) radians.

### Final Answer:
The number of radians through which the wheel turns in one second is \(12\pi\) radians.

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