Question

Which of the following pairs has not the same dimension?

• A. Stress; pressure
• B. Force; surface tension
• C. Impulse; linear momentum
• D. Frequency; angular velocity

Answer 1

Answer: (B)

Force; surface tension

Surface Tension$\left(T\right)=\frac{Force}{Length}$ . . . . . (1)

Since, $Force=Mass\times Acceleration$

And, $Acceleration=\frac{velocity}{time}=\left[L{T}^{-2}\right]$

$\therefore$ The dimensional formula of force $=M^1{L}^1{T}^{-2}$ . . . . (2)

On substituting equation (2) in equation (1) we get,

Surface Tension $\left(T\right)=\frac{Force}{Length}$

Or, $T=\frac{\left[M^1{L}^1{T}^{-2}\right]}{\left[L^1\right]}=M^1{T}^{-2}$

Therefore, surface tension is dimensionally represented as $\left[M^1{T}^{-2}\right]$

Dimension of force $=M^1{L}^1{T}^{-2}$

So the dimension of force and surface tension are different.