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?

Explanation

To find the unit of mass in the given system where the unit of force is 1 kN, unit of length is 1 km, and unit of time is 100 s, we can follow these steps:

### Step 1: Understand the relationship between force, mass, and acceleration
The fundamental equation relating force (F), mass (m), and acceleration (a) is given by Newton's second law:
\[ F = m \cdot a \]

### Step 2: Express acceleration in terms of length and time
Acceleration is defined as the change in velocity per unit time. In terms of length (L) and time (T), acceleration can be expressed as:
\[ a = \frac{L}{T^2} \]
where L is the unit of length and T is the unit of time.

### Step 3: Substitute the units into the equation
In the new system:
- The unit of force \( F = 1 \text{ kN} = 1000 \text{ N} \)
- The unit of length \( L = 1 \text{ km} = 1000 \text{ m} \)
- The unit of time \( T = 100 \text{ s} \)

Now, substituting these values into the equation for force:
\[ 1000 \text{ N} = m \cdot \frac{1000 \text{ m}}{(100 \text{ s})^2} \]

### Step 4: Simplify the equation
Rearranging the equation to solve for mass \( m \):
\[ m = \frac{1000 \text{ N} \cdot (100 \text{ s})^2}{1000 \text{ m}} \]

### Step 5: Calculate the value
Now, substituting the values:
\[ m = \frac{1000 \cdot 10000}{1000} \]
\[ m = 10000 \text{ kg} \]

### Conclusion
Thus, the unit of mass in this new system is:
\[ m = 10^4 \text{ kg} \]

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