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

Solution

## The correct option is A Force; surface tensionSurface 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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