A U-tube is supported with its limbs vertical and is partly filled with water. If the internal diameters of the limbs are `1xx10^(-2)mand1xx10^(-4)m` respectively. What will be the difference in heights of water in the two limbs? (Surface tension of water is 0.07 N/m.)

Explanation

Let `h_(1)andh_(2)` be the heights of water columns in the limbs of radis `r_(1)andr_(2)`
Then, `h_(1)=(2Tcostheta)/(r_(1)dg)=(2xx0.07xxcos0^(@))/(0.5xx10^(-4)xx1000xx9.8)`
`=2.8xx10^(-3)m=0.028xx10^(-1)m`
Similarly `h_(2)=(2Tcostheta)/(r_(2)dg)=(2xx0.07xxcos0^(@))/(0.5xx10^(-2)xx1000xx9.8)`
`=2.8xx10^(-1)m`
Therefore difference in heights
`h_(2)-h_(1)=(2.8-0.028)xx10^(-1)m`
`=2.772xx10^(-1)m=9.277m`.