If the unit of force is 1 kN, unit of length 1 km and unit of time is 100s, what will be the unit of mass?

Options

A. 1000 kg
B. 1 kg
C. 10000 kg
D. 100 kg

Explanation

To solve the problem, we need to find the unit of mass given the units of force, length, and time. We will use the relationship between force, mass, and acceleration.

### Step-by-Step Solution:

1. **Identify the Given Units:**
- Unit of Force (F) = 1 kN = 1000 N
- Unit of Length (L) = 1 km = 1000 m
- Unit of Time (T) = 100 s

2. **Recall the Formula for Force:**
The formula for force is given by:
\[ F = m \cdot a \]
where \( m \) is mass and \( a \) is acceleration.

3. **Express Acceleration in Terms of Length and Time:**
Acceleration (a) is defined as:
\[ a = \frac{L}{T^2} \]
Substituting the given units:
\[ a = \frac{1 \text{ km}}{(100 \text{ s})^2} = \frac{1000 \text{ m}}{10000 \text{ s}^2} = \frac{1000}{10000} \text{ m/s}^2 = 0.1 \text{ m/s}^2 \]

4. **Substituting Values into the Force Equation:**
Now substituting the values of force and acceleration into the force equation:
\[ 1000 \text{ N} = m \cdot 0.1 \text{ m/s}^2 \]

5. **Solving for Mass (m):**
Rearranging the equation to solve for mass:
\[ m = \frac{1000 \text{ N}}{0.1 \text{ m/s}^2} = 10000 \text{ kg} \]

6. **Conclusion:**
Therefore, the unit of mass is:
\[ m = 10^4 \text{ kg} \]

### Final Answer:
The unit of mass is **10,000 kg** or \( 10^4 \text{ kg} \).

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