Ncert Exercises & Solutions

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

1.	work and torque
2.	angular momentum and Planck's constant
3.	tension and surface tension
4.	impulse and linear momentum

(3) Hint: Use the concept of dimensions.

Step 1: Find the dimensions of each quantity in each option.

(a) Work = force x distance $= [{MLT}^{- 2}] [L] [{ML}^{2} T^{- 2}]$
Torque = force x distance $= [{ML}^{2} T^{- 2}]$

(b) Angular momentum $= mvr = [M] [{LT}^{1}] [L] = [{ML}^{2} T^{- 1}]$
Planck's constant $= \frac{E}{V} = \frac{[M L^{2} T^{- 2}]}{[T^{- 1}]} = [M L^{2} T^{- 1}]$

(c) Tension = force $= [{MLT}^{- 2}]$
Surface tension $= \frac{force}{length} = \frac{[{MLT}^{- 2}]}{[L]} = [{ML}^{0} T^{- 2}]$

(d) Impulse $= force \times time = [{MLT}^{- 2}] [Π] = [{MLT}^{- 1}]$
Momentum $= mass \times velocity = [M] [{LT}^{- 1}] = [{MLT}^{- 1}]$

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