Single Choice

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

AWork and torque
BAngular momentum and plank's constant
CTension and surface tension
Correct Answer
DImpulse and linear momentum

Solution

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. $$kg \ m^2s^{-1}$$
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.

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