Question

Out of the following pairs, choose the pair in which the physical quantities do not have identical dimension?

• A. Planck's constant and Angular momentum
• B. Pressure and Young's modules
• C. Impulse and moment of force
• D. Force and rate of change of linear momentum

Answer 1

Answer: (C)

(A) : Young's modulus is given by $Y=\frac{F}{A}.\frac{\Delta L}{L}$
This implies Pressure $\left(F/A\right)$ and Young's modulus have same dimensions.
(B) :
From the equation $L=\frac{nh}{2\pi }$
We say that, Planck's constant and angular momentum have same dimensions.
(C) : Using the relation between impulse $J$ and moment of force $\tau$, $J=\tau \Delta t$
We say that impulse and moment of force have different dimensions.
(D) :
From the relation $F=\frac{dP}{dt}$
We say that force $F$ and rate of change of momentum $\frac{dP}{dt}$ have same dimension.