Water Rises In A Capillary Tube To A Height 2.0 Cm. In An Another Capillary Whose Radius Is One-third Of It, How Much The Water Will Rise? If The First Capillary Is Inclined At An Angle Of 60o with The Vertical Then What Will Be The Position Of Water In The Tube?   

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Question

Water rises in a capillary tube to a height 2.0 cm. In an another capillary whose radius is one-third of it, how much the water will rise? If the first capillary is inclined at an angle of 60o with the vertical then what will be the position of water in the tube?   

Solution

Correct option is

4.0 cm

Height of water-column in a capillary of radius of r is, in usual notations, gives by 

         

or    hr = constant         

In a capillary tube of radius one-third (r/3), water will rise more. Suppose it rises to a height h’. Then 

       

      

            

When the first capillary is inclined at an angle 60o to the vertical, the vertical height h(= 2.0 cm) of the liquid will remain the same. Thus if the length of water in the capillary be h’ cm, then from the figure, we have  

         

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