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

Question

Which of the following pairs of physical quantities does not have same dimensional formula ? (A) Work and torque (B) Angular momentum and Planck’s constant (C) Tension and surface tension (D) Impulse and linear momentum

Tardigrade Admin · Accepted Answer

[ Tension ]=[ M L T -2] [ Surface Tension ]=([ M L T -2]/[ L ])=[ M L 0 T -2]

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

Work and torque

Angular momentum and Planck’s constant

Tension and surface tension

Impulse and linear momentum

$[$ Tension $] = [M L T^{- 2}]$
$[$ Surface Tension $] = \frac{[ M L T ^{- 2} ]}{[ L ]} = [M L^{0} T^{- 2}]$

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

Work and torque

Angular momentum and Planck’s constant

Tension and surface tension

Impulse and linear momentum

[ Tension ]=[MLT−2] [ Surface Tension ]=[L][MLT−2]​=[ML0T−2]

$[$ Tension $] = [M L T^{- 2}]$
$[$ Surface Tension $] = \frac{[ M L T ^{- 2} ]}{[ L ]} = [M L^{0} T^{- 2}]$