Question

Which of the following pairs of physical quantities does not have same dimensional formula?

Answer 1

Correct option is C. Tension and surface tension
a) Work =$$F \times \Delta x=[MLT^{-2}[L]=[ML^2T^{-2}]]$$

Torque=force $$\times$$ distance =$$[ML^2T^{-2}]$$

b) Angular momentum$$mvr=[M][LT^{1}][L]=[ML^2T^{-1}]$$

Plank's constant=$$\dfrac{E}{V}=\dfrac{[ML^2T^{-2}]}{[T^{-1}]}=[ML^2T^{-1}]$$

c) Tension (force)=$$[MLT^{-2}]$$

Surface tension =$$\dfrac{force}{length}=\dfrac{[MLT^{-2}]}{[L]}=[ML^0T^{-2}]$$

d) Impulse $$=F \times \Delta t=[MLT^{-2}][T]=[MLT^{-1}]$$

Momentum =$$mass \times velocity=[M][LT^{-1}]=[MLT^{-1}]$$

So, among the above pairs only tension and surface tension does not have the same dimensional formula. They both sound similar but they both have different meaning and different applications.