On the application of a constant torque , a wheel is turned from rest through 400 radians in 10 s. The angular acceleration is :

Options

A. (a)`8 rad s^(-2)`
B. (b)`5 rad s^(-2)`
C. (c)`6 rad s^(-2)`
D. (d)`7 rad s^(-2)`

Answer

To solve the problem of finding the angular acceleration of a wheel turned through 400 radians in 10 seconds from rest, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Angular displacement (θ) = 400 radians
- Initial angular velocity (u) = 0 radians/second (since it starts from rest)
- Time (t) = 10 seconds

2. **Use the Angular Motion Equation**:
The equation relating angular displacement, initial angular velocity, angular acceleration (α), and time is:
\[ \theta = ut + \frac{1}{2} \alpha t^2 \]
Since the initial angular velocity (u) is 0, the equation simplifies to:
\[ \theta = \frac{1}{2} \alpha t^2 \]

3. **Substitute the Known Values**:
Substitute θ = 400 radians and t = 10 seconds into the equation:
\[ 400 = \frac{1}{2} \alpha (10^2) \]
This simplifies to:
\[ 400 = \frac{1}{2} \alpha (100) \]

4. **Solve for Angular Acceleration (α)**:
Rearranging the equation gives:
\[ 400 = 50 \alpha \]
To find α, divide both sides by 50:
\[ \alpha = \frac{400}{50} = 8 \text{ radians/second}^2 \]

5. **Conclusion**:
The angular acceleration of the wheel is:
\[ \alpha = 8 \text{ radians/second}^2 \]

### Final Answer:
The angular acceleration is 8 radians/second².

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