Question

Which of the following pair does not have same dimensions ?

• A. Impulse, Torque
• B. Angular velocity, Velocity gradient
• C. Surface tension, Force constant
• D. Pressure, Modulus of Elasticity

Answer 1

Answer: (A)

Pressure $=$ Modulus of Elasticity $=\frac{F}{A}=M^1{L}^{-1}{T}^{-2}$
Angular velocity $=\omega =T^{-1}$

Velocity gradient $=\frac{dv}{dz}=\frac{L{T}^{-1}}{L}=T^{-1}$
Surface Tenstion $=\frac{f}{l}=$ Force constant $=\frac{M^1{L}^1{T}^{-2}}{L^1}=M{T}^{-2}$
Impulse $=f\times t=M^1{L}^1{T}^{-2}\times T^1=M^1{L}^1{T}^{-1}$
Torque $=\overrightarrow{r}\times \overrightarrow{f}=L^1\times M^1{L}^1{T}^{-2}=M^1{L}^2{T}^{-2}$
Hence, option D is correct.