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 follow these steps:

### Step 1: Identify Given Data
- Force (F) = 10 N
- Radius (r) = 0.5 m
- Moment of Inertia (I) = 2 kg·m²
- Initial Angular Velocity (ω₀) = 0 rad/s
- Time (t) = 2 s

### Step 2: Calculate the Torque (τ)
Torque is calculated using the formula:
\[ \tau = F \cdot r \]
Substituting the given values:
\[ \tau = 10 \, \text{N} \cdot 0.5 \, \text{m} = 5 \, \text{N·m} \]

### Step 3: Calculate Angular Acceleration (α)
Using the relation between torque and angular acceleration:
\[ \tau = I \cdot \alpha \implies \alpha = \frac{\tau}{I} \]
Substituting the values:
\[ \alpha = \frac{5 \, \text{N·m}}{2 \, \text{kg·m²}} = 2.5 \, \text{rad/s²} \]

### Step 4: Use Angular Displacement Formula
The angular displacement (θ) can be calculated using the formula:
\[ \theta = \omega_0 \cdot t + \frac{1}{2} \alpha \cdot t^2 \]
Since the initial angular velocity (ω₀) is 0:
\[ \theta = 0 + \frac{1}{2} \cdot 2.5 \, \text{rad/s²} \cdot (2 \, \text{s})^2 \]
Calculating further:
\[ \theta = \frac{1}{2} \cdot 2.5 \cdot 4 = \frac{10}{2} = 5 \, \text{radians} \]

### Final Answer
The angular displacement of the disc in the first two seconds is:
\[ \theta = 5 \, \text{radians} \]

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