Question

Which of the following pairs does not have similar dimensions?

• A. Tension and surface tension
• B. Stress and pressure
• C. Planck's constant and angular momentum
• D. Angle and strain

Answer 1

The correct option is A Tension and 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 $\left[M^1{T}^{-2}\right]$

Tension is defined as the magnitude of force.

$\therefore$ Demension of Tension $=$ Dimension of Force

So, dimension of tension $=M^1{L}^1{T}^{-2}$

So the dimension of tension and surface tension is different