Two tubes of same length and diameters 4mm and 8mm are joined together to form a U-shaped tube open at both the ends. If the U-tube contains water, then the difference between the levels of water in the two lims of the tube is
(Surface tension of water at the temperature of experiment is `7.3 xx 10^(-2) Nm^(-1)`, angle of contact `= 0^(@)`, density of water `= 1.0 xx 10^(3) kg m^(-3)` and acceleration due to gravity `= 10 ms^(-2)`)

Options

A. 3.65 mm
B. 36.5 mm
C. `0.365 mm`
D. 365 mm

Answer

A

Explanation

A figure of U-shaped tube of different diameter is given below,

Given, radius of first tube, `R_(1) = 2` mm and radius of second tube, `R_(2) = 4` mm.
density of water, `rho = 1.0 xx 10^(3) kg - m^(-3)`
Since, the tube is open at both the ends. So, `p_(A) = p_(B) = p_(0)` (atmospheric pressure)
Pressure in capillary tube B,
`p_(B) = (2T)/(R_(2)) = p_(0)`
[Here, T = Surface tension of water]
Similarly pressure at capillary tube A,
`p_(A) = (2T)/(R_(1)) = p_(0)`
Hence, for same height OO.,
`rho g x + (2T)/(R_(1)) = (2T)/(R_(2))`
`x = (2T)/(rho g)[(1)/(R_(1)) - (1)/(R_(2))]`
Putting the given values, we get
`x = (2 xx 7.3 xx 10^(-2))/(10^(3) xx 10 xx 10^(-3)) [(1)/(2) - (1)/(4)] = 3.65` mm
Hence, the difference between the levels of water in the two limbs of the tube is 3.65 mm. So, the correct option is (a).