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

Options

A. 2 times the original
B. 4 times the original
C. `(1)/(4)` times the original
D. `(1)/(2)` times the original

Explanation

To solve the problem, we need to understand the relationship between force, length, and energy. Let's break it down step by step:

### Step 1: Understanding the relationship between work and energy
Energy is defined as the capacity to do work. The work done (W) is given by the formula:
\[ W = F \times d \]
where \( F \) is the force applied and \( d \) is the distance moved in the direction of the force.

### Step 2: Identifying the units of force and length
The SI unit of force is Newton (N), and the SI unit of length is meter (m). Therefore, the unit of work (or energy) in SI units is:
\[ \text{Energy (or Work)} = \text{Force} \times \text{Distance} = \text{N} \times \text{m} = \text{N m} \]

### Step 3: Doubling the units of force and length
According to the problem, both the units of force and length are doubled. So, we have:
- New unit of force = \( 2F \) (where \( F \) is the original unit of force)
- New unit of length = \( 2d \) (where \( d \) is the original unit of length)

### Step 4: Calculating the new unit of energy
Now, substituting the new units into the work formula:
\[ \text{New Energy} = (2F) \times (2d) \]
\[ \text{New Energy} = 4 \times (F \times d) \]
Since \( F \times d \) is the original unit of energy, we can write:
\[ \text{New Energy} = 4 \times \text{(Original Energy)} \]

### Step 5: Conclusion
Thus, 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 **four times the original**.

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