Which of the statement are correct?

Options

A. Physical quantity represented by work in joule is `kg m^(2) s^(-2)`
B. physical quantity represented by force in newton is `kg m^(2) S^(-1)`
C. physical quantity represented by work in joule is `kg m s^(-2)`
D. Physical quantity represented by fore in newton is `kg m^(2) s^(-2)`

Answer

To determine which of the statements regarding physical quantities are correct, we need to analyze each statement based on the definitions and units of work and force.

### Step-by-Step Solution:

1. **Understanding Force**:
- The formula for force (F) is given by Newton's second law:
\[ F = m \cdot a \]
where \(m\) is mass and \(a\) is acceleration.
- The unit of mass (m) is kilograms (kg) and the unit of acceleration (a) is meters per second squared (m/s²).
- Therefore, the unit of force in SI units is:
\[ \text{Force (F)} = \text{kg} \cdot \text{m/s}^2 = \text{kg m/s}^2 \]
- This unit is also known as a Newton (N).

2. **Analyzing the Statements about Force**:
- **Statement 1**: "The physical quantity represented by force in newton is kilogram meter square per second."
- This statement is incorrect because the correct unit is kg m/s², not kg m²/s.
- **Statement 2**: "The physical quantity represented by force in newton is kilogram meter square per second square."
- This statement is also incorrect because the correct unit is kg m/s², not kg m²/s².

3. **Understanding Work**:
- The formula for work (W) is given by:
\[ W = F \cdot d \]
where \(F\) is force and \(d\) is displacement.
- The unit of displacement (d) is meters (m).
- Therefore, the unit of work in SI units is:
\[ \text{Work (W)} = \text{Force (F)} \cdot \text{Distance (d)} = \text{kg m/s}^2 \cdot \text{m} = \text{kg m}^2/\text{s}^2 \]
- This unit is also known as a Joule (J).

4. **Analyzing the Statements about Work**:
- **Statement 3**: "The physical quantity represented by work in joule is kilogram meter per second square."
- This statement is incorrect because the correct unit is kg m²/s², not kg m/s².
- **Statement 4**: "The physical quantity represented by work in joule is kilogram meter square per second square."
- This statement is correct because the unit of work is indeed kg m²/s².

### Conclusion:
- The correct statements are:
- **Only Statement 4** is correct: "The physical quantity represented by work in joule is kilogram meter square per second square."

### Summary of Correctness:
- Statement 1: Incorrect
- Statement 2: Incorrect
- Statement 3: Incorrect
- Statement 4: Correct