Which of the following pairs do not correctly matched ?

Options

A. Rotational power (Joule/sec)
B. Torque (Newton meter)
C. Angular displacement (radian)
D. Angular acceleration (radian/sec)

Answer

To determine which of the following pairs do not match correctly, we will analyze each option provided in the question.

### Step-by-Step Solution:

1. **Understanding Power**:
- Power is defined as the rate of doing work or the rate of transfer of energy.
- The formula for power is given by:
\[ \text{Power} = \frac{\text{Work}}{\text{Time}} \]
- The unit of work is Joules (J), and the unit of time is seconds (s).
- Therefore, the unit of power is:
\[ \text{Unit of Power} = \frac{\text{Joules}}{\text{seconds}} = \text{Watts (W)} \]
- **Conclusion**: The pairing for power is correct.

2. **Understanding Torque**:
- Torque (τ) is defined as the product of force (F) and the perpendicular distance (r) from the pivot point.
- The formula for torque is:
\[ \tau = F \times r \]
- The unit of force is Newtons (N), and the unit of distance is meters (m).
- Therefore, the unit of torque is:
\[ \text{Unit of Torque} = \text{N} \cdot \text{m} = \text{Newton meter (N m)} \]
- **Conclusion**: The pairing for torque is correct.

3. **Understanding Angular Displacement**:
- Angular displacement is the angle through which an object has rotated about a fixed point.
- It can be measured in radians or degrees.
- **Conclusion**: The pairing for angular displacement is correct.

4. **Understanding Angular Acceleration**:
- Angular acceleration (α) is defined as the rate of change of angular velocity (ω) with respect to time (t).
- The formula for angular acceleration is:
\[ \alpha = \frac{d\omega}{dt} \]
- The unit of angular velocity is radians per second (rad/s), and the unit of time is seconds (s).
- Therefore, the unit of angular acceleration is:
\[ \text{Unit of Angular Acceleration} = \frac{\text{rad/s}}{\text{s}} = \text{radians per second squared (rad/s}^2\text{)} \]
- However, if the pairing states that angular acceleration is measured in radians per second (rad/s), this is incorrect.
- **Conclusion**: The pairing for angular acceleration is incorrect.

### Final Answer:
The pair that does not match correctly is **D: Angular acceleration - radian per second**.