If the unit of force were 10N, that of power were 1 MW and that of time were 1 millisecond then the unit of length would be 

Options

A. `1 m`
B. `100 m`
C. `10^3 m`
D. `10^(-2) m`

Answer

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

### Step-by-Step Solution:

1. **Understand the relationship between power, force, and velocity**:
The formula for power (P) is given by:
\[ P = F \cdot v \]
where \( F \) is the force and \( v \) is the velocity. Velocity can also be expressed as distance (length, \( L \)) divided by time (\( t \)):
\[ v = \frac{L}{t} \]
Therefore, we can rewrite the power equation as:
\[ P = F \cdot \frac{L}{t} \]

2. **Rearranging the equation**:
From the above equation, we can express length \( L \) as:
\[ L = \frac{P \cdot t}{F} \]

3. **Substituting the given values**:
We are given:
- Unit of force \( F = 10 \, \text{N} \)
- Unit of power \( P = 1 \, \text{MW} = 10^6 \, \text{W} \)
- Unit of time \( t = 1 \, \text{ms} = 10^{-3} \, \text{s} \)

Now substituting these values into the equation for \( L \):
\[ L = \frac{10^6 \, \text{W} \cdot 10^{-3} \, \text{s}}{10 \, \text{N}} \]

4. **Calculating the length**:
Simplifying the equation:
\[ L = \frac{10^6 \cdot 10^{-3}}{10} \]
\[ L = \frac{10^3}{10} = 10^2 \, \text{m} = 100 \, \text{m} \]

5. **Conclusion**:
Therefore, the unit of length is \( 100 \, \text{meters} \).

### Final Answer:
The unit of length is **100 meters**.

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