Question

Which pair do not have equal dimensions?

• A. Energy and torque
• B. Force and impulse
• C. Angular momentum and Planck's constant
• D. Elastic modulus and pressure

Answer 1

Answer: (B)

For $\left(A\right):-$ Energy $=kg.m^2.s^2=\left[M{L}^2{T}^{-2}\right]$

Torque $=kg.m^2.s^2=\left[M{L}^2{T}^{-2}\right]$

For $\left(B\right):-$ Force $=kg\times m/s^2=\left[{MLT}^{-2}\right]$

Impulse$=kgm/s=\left[{MLT}^{-1}\right]$

For $\left(C\right):-$ Angular momentum $=kg{m}^2/s=\left[{ML}^2{T}^{-1}\right]$

Planck's constant$=kg{m}^2/s=\left[{ML}^2{T}^{-1}\right]$

For $\left(D\right):-$ Elastic modulus$=kg/m^2=\left[{ML}^{-2}\right]$

Pressure$=kg/m^2=\left[{ML}^{-2}\right]$

From the above data, only Force and Impulse does not have equal dimensions.