Which of the following units are not correct for the physical quantity ?

Options

A. Acceleration: `ms^(2)`
B. Pressure: `kg m^(-2)s^(-2)`
C. Power: Js
D. Frequency: `s^(-1)`

Answer

To determine which of the given units are not correct for their respective physical quantities, we will analyze each option step by step.

### Step 1: Analyze Acceleration
- **Definition**: Acceleration is defined as the rate of change of velocity.
- **Formula**: Acceleration (a) = Velocity (v) / Time (t)
- **Units**:
- Velocity (v) is measured in meters per second (m/s).
- Time (t) is measured in seconds (s).
- **Unit of Acceleration**:
\[ \text{Unit of Acceleration} = \frac{\text{Velocity}}{\text{Time}} = \frac{\text{m/s}}{\text{s}} = \text{m/s}^2 \]
- **Conclusion**: The unit given for acceleration is correct: m/s².

### Step 2: Analyze Pressure
- **Definition**: Pressure is defined as force per unit area.
- **Formula**: Pressure (P) = Force (F) / Area (A)
- **Units**:
- Force (F) can be expressed as mass (m) times acceleration (a), so F = m * a.
- Mass (m) is measured in kilograms (kg), and acceleration (a) is measured in m/s².
- Area (A) is measured in square meters (m²).
- **Unit of Pressure**:
\[ \text{Unit of Pressure} = \frac{\text{Force}}{\text{Area}} = \frac{m \cdot a}{A} = \frac{\text{kg} \cdot \text{m/s}^2}{\text{m}^2} = \frac{\text{kg}}{\text{m} \cdot \text{s}^2} \]
- **Conclusion**: The unit given for pressure is incorrect. The correct unit is kg/(m·s²).

### Step 3: Analyze Power
- **Definition**: Power is defined as the rate at which work is done.
- **Formula**: Power (P) = Work (W) / Time (t)
- **Units**:
- Work (W) is defined as force times displacement, W = F * d.
- Force (F) is kg·m/s², and displacement (d) is in meters (m).
- **Unit of Power**:
\[ \text{Unit of Power} = \frac{\text{Work}}{\text{Time}} = \frac{F \cdot d}{t} = \frac{(kg \cdot m/s^2) \cdot m}{s} = \frac{kg \cdot m^2}{s^3} \]
- **Conclusion**: The unit given for power is incorrect. The correct unit is kg·m²/s³ (or Watts).

### Step 4: Analyze Frequency
- **Definition**: Frequency is defined as the number of occurrences of a repeating event per unit time.
- **Formula**: Frequency (f) = 1 / Time period (T)
- **Units**:
- Time period (T) is measured in seconds (s).
- **Unit of Frequency**:
\[ \text{Unit of Frequency} = \frac{1}{\text{s}} = \text{s}^{-1} \]
- **Conclusion**: The unit given for frequency is correct: s⁻¹.

### Final Conclusion
- The units that are not correct for the physical quantities are:
- Pressure: kg/(m·s²) is the correct unit, not the one given.
- Power: kg·m²/s³ (Watts) is the correct unit, not the one given.

### Summary of Incorrect Units
1. Pressure: Incorrect
2. Power: Incorrect
3. Acceleration: Correct
4. Frequency: Correct