In the above question, the value of its angular velocity after 2 seconds will be:

Options

A. 2.5 rad/sec
B. 5 rad/sec
C. 10 rad/sec
D. 20 rad/sec

Answer

To solve the problem of finding the angular velocity of the disc after 2 seconds, we can follow these steps:

### Step 1: Identify the known values
- Moment of inertia \( I = 2 \, \text{kg m}^2 \)
- Force applied \( F = 10 \, \text{N} \)
- Radius of the disc \( R = 0.5 \, \text{m} \)
- Time \( T = 2 \, \text{s} \)

### Step 2: Calculate the torque
Using the formula for torque:
\[ \tau = R \times F \]
Substituting the known values:
\[ \tau = 0.5 \, \text{m} \times 10 \, \text{N} = 5 \, \text{N m} \]

### Step 3: Calculate the angular acceleration
Using the relationship between torque and angular acceleration:
\[ \tau = I \alpha \]
Rearranging for angular acceleration \( \alpha \):
\[ \alpha = \frac{\tau}{I} = \frac{5 \, \text{N m}}{2 \, \text{kg m}^2} = 2.5 \, \text{rad/s}^2 \]

### Step 4: Use the angular motion equation to find final angular velocity
The equation relating initial angular velocity, angular acceleration, and time is:
\[ \omega_f = \omega_0 + \alpha T \]
Assuming the initial angular velocity \( \omega_0 = 0 \) (the disc starts from rest):
\[ \omega_f = 0 + (2.5 \, \text{rad/s}^2)(2 \, \text{s}) = 5 \, \text{rad/s} \]

### Step 5: Conclusion
The angular velocity of the disc after 2 seconds is:
\[ \omega_f = 5 \, \text{rad/s} \]