Two narrow bores of diameters 3.0mm and 6.0 mm are joined together to form a U-shaped tube open at both ends. If th U-tube contains water, what is the difference in its levels in the two limbs of the tube? Surface tension of water at the temperature of the experiment is `7.3xx10^(-2)Nm^(-1)`. Take the angle of contact to be zero. and density of water to be `1.0xx10^(3)kg//m^(3)`.
`(g=9.8 ms^(-2))`

Options

A. 4 mm
B. 5 mm
C. 8 mm
D. 3 mm

Answer

B

Explanation

Let `h_(1) and h_(2) ` be the heights upto which water rises in the two limbs of the U tube .
Then `h_(1) = (2Tcos theta)/(r_(1)rhog) and h_(2) = (2T cos theta)/(r_(2)rhog)`
`r_(1) = 1.5 xx 10^(-3) and r_(2) = 3 xx 10^(-3) m `
` :' r_(1) lt r_(2), h_(1) gt h_(2)`
For water , `theta = 0^(@) , cos theta = 1 `
` :. h_(1) - h_(2) = (2T)/(rhog) [ 1/(r_(1))-1/(r_(2))] `
` = (2 xx 7.5 xx 10^(-2))/(10^(3) xx 10 ) [(10^(3))/(1.5) - (10^(3))/3] `
` = 15 xx 10^(-3) [ (3-1.5)/(3 xx 1.5) ] `
` = 5 xx 10^(-3) m = 5 ` mm