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

  1. Work and torque.
  2. Angular momentum and Planck’s constant.
  3. Tension and surface tension.
  4. Impulse and linear momentum.

Answer (Detailed Solution Below)

Option 3 : Tension and surface tension.

Detailed Solution

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EXPLANATION:

1) Work = Force × Displacement = [MLT-2× [L] = [ML2T-2] 

Torque = Force × perpendicular distance = [MLT-2× [L] = [ML2T-2] 

2) Angular momentum = mvr = [M] × [LT-1] × [L] = [ML2T-1] 

We know, E = hν [E = energy, ν = frequency]

Plank's constant = E/ν = [ML2T-2]/[T-1] = [ML2T-1] 

3) Tension = Force = [MLT-2]

surface tension = Force/length = [MLT-2]/[L] = [ML0T-2]

4) Impulse = Force × time interval = [MLT-2] × [T] =[MLT-1]

Momentum = mass × velocity = [M] × [LT-1] = [MLT-1]

So, only in (c) both the dimensions are not matching.

So, the correct answer is option (3).

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