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Question

derive the expression for height of which the liquid rise in a capillary tube of radius r. explain what happens when the length of the capillary tube is less than the height up to which the liquid may rise in it.

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Solution

Let the radius of the glass capillary tube be r, the coefficient of surface tension of the liquid he T, the density of the liquid be ρ, the angle of contact between the liquid and the walls of the tube be θ and the height to which the liquid rises in the tube be h. now weight of the liquid coloumn = πr2ρghnow due to surafce tension the force will act on the liquid coloumn which is the vertical component of the surface tension force is= 2πrcosθTequating these two we can write2πrcosθT= πr2ρghso h=2Tcosθrρg is the elevation of the liquid through the coloumn,If the length of the tube L is smaller than the height up, then the water will come up the end but will not overflow as for overflowing it needs extra force which is not present here.

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