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NEET PHYSICSEasy

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

A

Increased 4 times

B

Increased 8 times

C

Increased 16 times

D

Decreased 16 times

Step-by-Step Solution

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