In the above question, angular displacement of the disc, in first two second will be in radian:

Options

A. 2.5
B. 5
C. 10
D. 20

Answer

To find the angular displacement of the disc in the first two seconds, we can use the kinematic equation for rotational motion. The equation we will use is:

\[ \theta = \omega_0 t + \frac{1}{2} \alpha t^2 \]

### Step-by-Step Solution:

1. **Identify Initial Angular Velocity (\(\omega_0\))**:
- The disc starts from rest, so the initial angular velocity \(\omega_0 = 0\) rad/s.

2. **Determine Angular Acceleration (\(\alpha\))**:
- From the previous calculations, we found that the angular acceleration \(\alpha = 2.5\) rad/s².

3. **Identify Time Interval (\(t\))**:
- We are interested in the first two seconds, so \(t = 2\) s.

4. **Substitute Values into the Equation**:
- Plugging the values into the equation:
\[ \theta = 0 \cdot 2 + \frac{1}{2} \cdot 2.5 \cdot (2)^2 \]

5. **Calculate the Angular Displacement**:
- Simplifying the equation:
\[ \theta = 0 + \frac{1}{2} \cdot 2.5 \cdot 4 \]
\[ \theta = \frac{1}{2} \cdot 10 = 5 \text{ radians} \]

### Final Answer:
The angular displacement of the disc in the first two seconds is **5 radians**.

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