Question:
Which of the following physical quantities has the same dimensions as surface tension?
Which of the following physical quantities has the same dimensions as surface tension?
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Surface tension can be written as force per length or energy per area. Both give the same dimensional formula \([MT^{-2}]\).
Updated On: Jun 3, 2026
- Force \(\times\) Length
- Energy Area
- Pressure \(\times\) Length
- Work \(\times\) Distance
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The Correct Option is B
Solution and Explanation
Concept:
Surface tension is defined as force acting per unit length. So, \(\displaystyle \text{Surface tension}=\frac{\text{Force}}{\text{Length}}\)
Step 1: Find the dimensional formula of surface tension.
Force has dimensional formula: \(\displaystyle [F]=[MLT^{-2}]\) Length has dimensional formula: \(\displaystyle [L]\) Therefore, \(\displaystyle [\text{Surface tension}]=\frac{[MLT^{-2}]}{[L]}\) \(\displaystyle =[MT^{-2}]\)
Step 2: Check Energy per Area.
Energy has dimensional formula: \(\displaystyle [E]=[ML^2T^{-2}]\) Area has dimensional formula: \(\displaystyle [A]=[L^2]\) So, \(\displaystyle \left[\frac{\text{Energy}}{\text{Area}}\right]=\frac{[ML^2T^{-2}]}{[L^2]}\) \(\displaystyle =[MT^{-2}]\)
Step 3: Compare both dimensions.
Surface tension: \(\displaystyle [MT^{-2}]\) Energy per area: \(\displaystyle [MT^{-2}]\) Both are the same.
Step 4: Final conclusion.
Hence, the correct answer is: \(\displaystyle \boxed{\text{Energy / Area}}\)
Surface tension is defined as force acting per unit length. So, \(\displaystyle \text{Surface tension}=\frac{\text{Force}}{\text{Length}}\)
Step 1: Find the dimensional formula of surface tension.
Force has dimensional formula: \(\displaystyle [F]=[MLT^{-2}]\) Length has dimensional formula: \(\displaystyle [L]\) Therefore, \(\displaystyle [\text{Surface tension}]=\frac{[MLT^{-2}]}{[L]}\) \(\displaystyle =[MT^{-2}]\)
Step 2: Check Energy per Area.
Energy has dimensional formula: \(\displaystyle [E]=[ML^2T^{-2}]\) Area has dimensional formula: \(\displaystyle [A]=[L^2]\) So, \(\displaystyle \left[\frac{\text{Energy}}{\text{Area}}\right]=\frac{[ML^2T^{-2}]}{[L^2]}\) \(\displaystyle =[MT^{-2}]\)
Step 3: Compare both dimensions.
Surface tension: \(\displaystyle [MT^{-2}]\) Energy per area: \(\displaystyle [MT^{-2}]\) Both are the same.
Step 4: Final conclusion.
Hence, the correct answer is: \(\displaystyle \boxed{\text{Energy / Area}}\)
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