Which one of the following is not measured in the units of energy

Options

A. (couple) `xx` (angle turned through)
B. moment of inertia `xx ("angular velocity")^(2)`
C. Force `xx` distance
D. impulse `xx` time

Answer

To solve the question "Which one of the following is not measured in the units of energy?", we will analyze the dimensions of various physical quantities and compare them with the dimension of energy.

### Step-by-Step Solution:

1. **Understand the Unit of Energy**:
- The standard unit of energy is the Joule (J).
- The dimension of energy can be expressed as:
\[ [E] = [M][L^2][T^{-2}] \]
where \( M \) is mass, \( L \) is length, and \( T \) is time.

2. **Identify the Given Options**:
- We need to evaluate the dimensions of the following quantities:
1. Couple
2. Moment of Inertia × Angular Velocity
3. Work
4. Impulse × Time

3. **Calculate the Dimension of Each Quantity**:
- **Couple**:
- A couple is defined as the product of force and the distance (moment arm).
- The dimension of force is:
\[ [F] = [M][L][T^{-2}] \]
- Therefore, the dimension of couple is:
\[ [Couple] = [F][L] = [M][L][T^{-2}][L] = [M][L^2][T^{-2}] \]
- This matches the dimension of energy.

- **Moment of Inertia × Angular Velocity**:
- Moment of Inertia \( I \) has the dimension:
\[ [I] = [M][L^2] \]
- Angular velocity \( \omega \) has the dimension:
\[ [\omega] = [T^{-1}] \]
- Therefore, the dimension of Moment of Inertia × Angular Velocity is:
\[ [I \cdot \omega] = [M][L^2][T^{-1}] = [M][L^2][T^{-2}] \]
- This also matches the dimension of energy.

- **Work**:
- Work is defined as force multiplied by displacement.
- Since we already calculated the dimension of force, we can say:
\[ [Work] = [F][L] = [M][L][T^{-2}][L] = [M][L^2][T^{-2}] \]
- This matches the dimension of energy.

- **Impulse × Time**:
- Impulse is defined as force multiplied by time:
\[ [Impulse] = [F][T] = [M][L][T^{-2}][T] = [M][L][T^{-1}] \]
- Therefore, the dimension of Impulse × Time is:
\[ [Impulse \cdot T] = [M][L][T^{-1}][T] = [M][L] \]
- This does not match the dimension of energy.

4. **Conclusion**:
- The only quantity that does not have the dimension of energy is **Impulse × Time**. Therefore, the answer to the question is that **Impulse × Time is not measured in the units of energy**.