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Question

Which of the following pairs has not the same dimension?

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

The correct option is A Force; surface tension

Surface Tension(T)=ForceLength . . . . . (1)

Since, Force=Mass×Acceleration

And, Acceleration=velocitytime=[LT2]

The dimensional formula of force =M1L1T2 . . . . (2)

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

Surface Tension (T)=ForceLength

Or, T=[M1L1T2][L1]=M1T2

Therefore, surface tension is dimensionally represented as [M1T2]


Dimension of force =M1L1T2

So the dimension of force and surface tension are different.


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