A fly wheel of `0.4 kg(m^-2)` M.I. and of 0.2 m radius can rotate about its axis. A rope is wrapped around its circumference and pulled with 10 N force. The value of angular acceleration in `rad/sec^2`will be?

Options

A. 5
B. 2
C. 10
D. 0.8

Answer

To find the angular acceleration of the flywheel, we will follow these steps:

### Step 1: Identify the given values
- Moment of Inertia (I) = 0.4 kg·m²
- Radius (r) = 0.2 m
- Force (F) = 10 N

### Step 2: Calculate the torque (τ)
Torque is calculated using the formula:
\[ \tau = F \times r \]
Substituting the given values:
\[ \tau = 10 \, \text{N} \times 0.2 \, \text{m} = 2 \, \text{N·m} \]

### Step 3: Use the relationship between torque and angular acceleration
The relationship between torque (τ), moment of inertia (I), and angular acceleration (α) is given by:
\[ \tau = I \times \alpha \]
We can rearrange this formula to solve for angular acceleration (α):
\[ \alpha = \frac{\tau}{I} \]

### Step 4: Substitute the values into the equation
Substituting the values of torque and moment of inertia into the equation:
\[ \alpha = \frac{2 \, \text{N·m}}{0.4 \, \text{kg·m²}} = 5 \, \text{rad/sec²} \]

### Step 5: Conclusion
The angular acceleration of the flywheel is:
\[ \alpha = 5 \, \text{rad/sec²} \]

---