A torque T acts on a body of moment of inertia l rotating with angular speed `omega`. It will be stopped just after time

Options

A. `(lT)/(omega)`
B. `(l omega)/(T)`
C. `(T omega)/(l)`
D. `l omega T`

Answer

To solve the problem, we need to find the time \( t \) it takes for a body with moment of inertia \( I \) and initial angular speed \( \omega \) to come to a stop when a torque \( T \) is applied.

### Step-by-Step Solution:

1. **Understanding the relationship between torque and angular acceleration**:
The torque \( T \) acting on a rotating body is related to its moment of inertia \( I \) and angular acceleration \( \alpha \) by the equation:
\[ T = I \alpha \]

2. **Expressing angular acceleration**:
From the equation above, we can express angular acceleration \( \alpha \) as:
\[ \alpha = \frac{T}{I} \]

3. **Using the angular kinematics equation**:
We know that the final angular velocity \( \omega' \) after time \( t \) can be expressed using the initial angular velocity \( \omega \), angular acceleration \( \alpha \), and time \( t \):
\[ \omega' = \omega + \alpha t \]
Since the body comes to a stop, the final angular velocity \( \omega' = 0 \). Therefore, we can write:
\[ 0 = \omega + \alpha t \]

4. **Substituting for angular acceleration**:
Substituting \( \alpha = \frac{T}{I} \) into the equation gives:
\[ 0 = \omega + \left(\frac{T}{I}\right) t \]

5. **Rearranging to find time \( t \)**:
Rearranging the equation to solve for \( t \):
\[ \frac{T}{I} t = -\omega \]
\[ t = -\frac{I \omega}{T} \]
Since time cannot be negative, we take the absolute value:
\[ t = \frac{I \omega}{T} \]

6. **Final expression for time**:
Thus, the time \( t \) it takes for the body to stop is given by:
\[ t = \frac{I \omega}{T} \]

### Conclusion:
The time taken for the body to stop when a torque \( T \) is applied is:
\[ t = \frac{I \omega}{T} \]