question_answer

A coaxial cylinder made of glass is immersed in a liquid of surface tension 'S? Radius of inner and outer surface of cylinder is \[{{R}_{1}}\] and \[{{R}_{2}},\] respectively. Height till which liquid will rise is (density of liquid is \[\rho \])

A) \[\frac{2S}{{{R}_{2}}\rho g}\]

B) \[\frac{2S}{{{R}_{1}}\rho g}\]

C)  \[\frac{S}{({{R}_{2}}-{{R}_{1}})\rho g}\]        

D) \[\frac{2S}{({{R}_{2}}-{{R}_{1}})\rho g}\]

Correct Answer: D

Solution :

[d] Net upward force \[=2\pi {{R}_{2}}S+2\pi {{R}_{1}}S\] [since contact angle\[=0{}^\circ \]] \[\therefore \] Capillary rise is given by \[h=\frac{2\pi S({{R}_{1}}+{{R}_{2}})}{\pi (R_{2}^{2}-R_{1}^{2})\rho g}=\frac{2S}{\left( {{R}_{2}}-{{R}_{1}} \right)\rho g}\]