If the unit of length and force be increased four times, then the unit of energy is:

Question

Accepted Answer

1. **Identify the Physical Relationship:** Energy (or Work) is defined as the product of Force and Displacement. Mathematically, $W = \mathbf{F} \cdot \mathbf{d}$. Therefore, the dimensional relationship is $[E] = [F][L]$.
2. **Analyze the Change:** The problem states that the unit of length is increased by a factor of 4 ($L' = 4L$) and the unit of force is increased by a factor of 4 ($F' = 4F$).
3. **Calculate the New Unit:** Substituting these new units into the dimensional equation for energy:
   $$E' = [F'][L'] = (4F)(4L) = 16(FL) = 16E$$
4. **Conclusion:** The new unit of energy is 16 times the original unit.

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