In the above question, if the disc executes rotatory motion, its angular acceleration will be:

Options

A. 2.5 `"rad"//"sec"^(2)`
B. 5 `"rad"//"sec"^(2)`
C. 10 `"rad"//"sec"^(2)`
D. 20 `"rad"//"sec"^(2)`

Answer

To solve the problem regarding the angular acceleration of a disc executing rotational motion, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Given Values:**
- Moment of Inertia (I) of the disc = 2 kg·m²
- Force (F) applied = 10 N
- Radius (r) of the disc = 0.5 m

2. **Calculate Torque (τ):**
Torque is calculated using the formula:
\[ \tau = r \times F \]
Since the force is applied perpendicularly to the radius, we can directly multiply:
\[ \tau = 0.5 \, \text{m} \times 10 \, \text{N} = 5 \, \text{N·m} \]

3. **Relate Torque to Angular Acceleration (α):**
The relationship between torque and angular acceleration is given by:
\[ \tau = I \cdot \alpha \]
Rearranging this gives:
\[ \alpha = \frac{\tau}{I} \]

4. **Substitute the Values:**
Now substitute the values of torque and moment of inertia into the equation:
\[ \alpha = \frac{5 \, \text{N·m}}{2 \, \text{kg·m²}} = 2.5 \, \text{rad/s²} \]

5. **Final Result:**
The angular acceleration of the disc is:
\[ \alpha = 2.5 \, \text{rad/s²} \]