A U tube is supported with its limbs vertical and is partly filled with water. If the inner diameter of the limbs are 1cm,and 0.01 cm , respectively, what will be the difference in height of water in the two limbs? S.T. or water `70 xx 10^(-3) Nm^(-1)`. Angle of contact , `theta = 0^(@)`.

Explanation

Here, ` 2r_(1)= 1 cm`
or ` r_(1)=1/2 cm = 1/200 m, 2 r_(2) = 0.01 cm`
or `r_(2)= (0.01)/(2)cm = (0.01)/(200)m`,
`S= 70 xx 10^(-3) N//m, theta= 0^(@)`
Let `h_(1) and h_(2)` be the heights to which water rises in wider and narrow tube respectively. Then
`h_(1)= (2 S cos theta)/(r_(1) rho g)`
and `h_(2)= (2 S cos theta)/(r_(2) rho g)`
Difference in levels of water in two limbs of U tube is
`h_(2)-h_(1)=(2 S cos theta)/(rho g) [(1)/(r_(2))-1/(r_(1))]`
`2 xx (70 xx 10^(-3) xx cos theta)/(10^(3) xx 9.8)`
`xx [(1)/((0.01//(200)-(1)/((1//200)))]]`
`=0.2829m`.