Which One Of The Following Relations Is Dimensionally Consistent Where h is Height To Which A Liquid Of Density ρ Rises In A Capillary Tube Of Radius, r, Tis The Surface Tension Of The Liquid, θ The Angle Of Contact And g the Acceleration Due To Gravity?

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Question

Which one of the following relations is dimensionally consistent where h is height to which a liquid of density ρ rises in a capillary tube of radius, rTis the surface tension of the liquid, θ the angle of contact and g the acceleration due to gravity?

Solution

Correct option is

Since cos θ is dimensionless, using the dimensions of Tr, ρ and g, it is easy to see that  is only one that is dimensionally consistent. The dimensions of h are the same as those of 

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