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What is capillarity? Obtain an expression for the surface tension of a liquid by capillary rise method.

Answer» <html><body><p></p>Solution :The rise or fall of a liquid in a narrow tube is called capillarity.<br/>Let us consider a <a href="https://interviewquestions.tuteehub.com/tag/capillary-908628" style="font-weight:bold;" target="_blank" title="Click to know more about CAPILLARY">CAPILLARY</a> tube which is <a href="https://interviewquestions.tuteehub.com/tag/held-7620091" style="font-weight:bold;" target="_blank" title="Click to know more about HELD">HELD</a> vertically in a beaker containing water, the water rises in the capillary tube to a height h due to surface tension.<br/><img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/PRE_GRG_PHY_XI_V02_C07_E01_054_S01.png" width="80%"/> <br/>The surface tension force `F_(T)` acts along the tangent at the point of contact downwards and its reaction force upwards. Surface tension T, is resolved into two components.<br/>(i) Horizontal <a href="https://interviewquestions.tuteehub.com/tag/component-926634" style="font-weight:bold;" target="_blank" title="Click to know more about COMPONENT">COMPONENT</a> T `sintheta` and <br/>(ii) Vertical component T `costheta` acting upwards, all along the whole circumference of the meniscus.<br/>Tota upward force `=(Tcostheta)(2pir)=2pirTcostheta` <br/>Where `theta` is the angle of contact, r is the radius of the tube. Let `<a href="https://interviewquestions.tuteehub.com/tag/rho-623364" style="font-weight:bold;" target="_blank" title="Click to know more about RHO">RHO</a>` be the density of water and h be the height to which the liquid rises inside the tube. Then,<br/>`{:(("the volume of"),("liquid column"),("in the tube,<a href="https://interviewquestions.tuteehub.com/tag/v-722631" style="font-weight:bold;" target="_blank" title="Click to know more about V">V</a>")):}={:(("volume of the"),("liquid column of"),("radius r height h")):}+{:(("volume of the liquid of radius"),("r and height h-volume of"),("the hemisphere of radius of r")):}` <br/>`V=pir^(2)h+(pir^(2)xxr-(2)/(3)pir^(3))` <br/>`rArrV=pir^(2)h+(1)/(3)pir^(3)` <br/>The upward force supports the weight of the liquid column above the free surface, therefore,<br/>`2pirTcostheta=pir^(2)(h+(1)/(3)r)rhog` <br/>`rArr""T=((h+(1)/(3)r)rhog)/(2costheta)` <br/>If the capillary is a very fine tube ofradius (i.e., radius is very small) then `(r)/(3)` can be neglected when it is compared to the height h. Therefore,<br/>`T=(rrhogh)/(2costheta)`</body></html>


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