A uniform capillary tube of length l and inner radius r with its end sealed is submerged vertically into water. The outside pressure is p_0 and surface tension of water is gamma. Whena length x of the capillary is submerged into water . It is found that water levels inside and outside the capillary coincide. The Value of x is

A uniform capillary tube of length l and inner radius r with its end s

1.	A uniform capillary tube of length l and inner radius r with its end sealed is submerged vertically into water. The outside pressure is p_0 and surface tension of water is gamma. Whena length x of the capillary is submerged into water . It is found that water levels inside and outside the capillary coincide. The Value of x is
Answer» `(L)/((1+(p_0r)/(4 gamma)))` `(l)/((1-(p_0r)/(4 gamma)))` `(l)/((1-(p_0r)/(2 gamma)))` `(l)/((1+(p_0r)/(2 gamma)))` Solution :When a length x of the CAPILLARY is SUBMERGED in water and the atmospheric PRESSURE in the capillary tube is `p.`. Then `p_0(lA)=p.(l-x)A` or, `p.=(p_0l)/(l-x)""…(1)` As the water levels inside and outside the capillary coincide, so `p.-p_0=(2gamma)/(r )""...(2)` Solving equation (1) and (2) we get, `x=(l)/(1+(p_0r)/(2gamma))`