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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$$ (T) =\dfrac{ Force}{Length}$$  . . . . . (1)

Since, $$Force = Mass \times Acceleration$$

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

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

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

Surface Tension $$(T) = \dfrac{Force}{  Length}$$

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

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


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

So the dimension of force and surface tension are different.


Physics

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