If the unit of length is doubled, unit of time is halved and unit of force is quadrupled, the unit of power would change by the factor

Options

A. `1//4`
B. `16`
C. `1/16`
D. `8`

Answer

To solve the problem, we need to analyze how the changes in the units of length, time, and force affect the unit of power.

### Step-by-Step Solution:

1. **Understanding the formula for power**:
The formula for power (P) is given by:
\[ P = \frac{F \cdot L}{T} \]
where \( F \) is force, \( L \) is length, and \( T \) is time.

2. **Identifying the changes in units**:
- The unit of length is doubled: \( L' = 2L \)
- The unit of time is halved: \( T' = \frac{T}{2} \)
- The unit of force is quadrupled: \( F' = 4F \)

3. **Substituting the new units into the power formula**:
Now we substitute the new units into the power formula:
\[ P' = \frac{F' \cdot L'}{T'} \]
Substituting the changes:
\[ P' = \frac{(4F) \cdot (2L)}{\frac{T}{2}} \]

4. **Simplifying the expression**:
Simplifying the equation:
\[ P' = \frac{4F \cdot 2L}{\frac{T}{2}} = \frac{8FL}{\frac{T}{2}} = 8FL \cdot \frac{2}{T} = 16 \cdot \frac{FL}{T} \]
Thus, we have:
\[ P' = 16P \]

5. **Conclusion**:
The unit of power would change by a factor of 16.

### Final Answer:
The unit of power would change by a factor of **16**.

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