If the units of force and length are doubled, then the unit of energy will be

Options

A. `1//4` times
B. `1//2` times
C. `2` times
D. `4` times

Answer

To solve the problem, we need to understand the relationship between force, length, and energy. The unit of energy can be expressed in terms of force and displacement (length).

### Step-by-Step Solution:

1. **Understanding the Units of Energy**:
- The unit of energy (E) is defined as the work done, which is given by the formula:
\[ E = \text{Force} \times \text{Displacement} \]
- In SI units, energy is measured in Joules (J), where 1 Joule = 1 Newton (N) × 1 meter (m).

2. **Identifying the Changes in Units**:
- According to the problem, both the units of force and length are doubled.
- Let the initial unit of force be \( F \) and the initial unit of length be \( L \).

3. **Calculating the New Units**:
- If the unit of force is doubled, the new unit of force becomes:
\[ F' = 2F \]
- If the unit of length is doubled, the new unit of length becomes:
\[ L' = 2L \]

4. **Substituting the New Units into the Energy Formula**:
- The new energy \( E' \) can be calculated using the new units:
\[ E' = F' \times L' = (2F) \times (2L) \]

5. **Simplifying the Expression**:
- Now, substituting the new values into the equation:
\[ E' = 2F \times 2L = 4FL \]
- This shows that the new unit of energy \( E' \) is four times the initial energy.

6. **Conclusion**:
- Therefore, if the units of force and length are both doubled, the unit of energy will be four times the original unit of energy.

### Final Answer:
The unit of energy will be \( 4 \times \text{(original unit of energy)} \).