Question

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

• A. Work and torque
• B. Angular momentum and plank's constant
• C. Tension and surface tension
• D. Impulse and linear momentum

Answer 1

The correct option is C Tension and surface tension

Work and torque both are represented as force multiplied by distance therefore must have the same dimensional formula.

Angular momentum can be written as $L=mvr$ which gives its dimensions i.e. $kg{m}^2{s}^{-1}$

and it is same as that of plank's constant.

As we know $E=h\nu$

$\therefore$ $h=E/\nu$

However tension which is defined as force and surface tension which is defined as force per unit length must have different dimensional formulas.

Impulse is change is linear momentum over a time interval, therefore has the same dimension as the linear momentum.