Question

Two narrow bores of diameter 5.0 mm and 8.0 mm are joined together to form a U-shaped tube open at both ends. If this U-tube contains water, what is the difference in the level of the two limbs, of the tube?

[Take surface tension of water T = 7.3 × 10^-2 Nm^-1, angle of contact = 0, g = 10 ms^-2 and density of water = 1.0 × 10³ kgm^-3]

विकल्प

• 5.34 mm

• 4.97 mm

• 2.19 mm

• 3.62 mm

Answer 1

2.19 mm

Explanation:

The finer bore (with a smaller radius) causes the water to rise to a greater height. As shown in the figure, let Δh height of the column be greater than the other bore.

Consider two points on the same level, A and B. As a result, the pressure will be the same. 

P_A = P_B

`P_"atm" - (2T)/r_1 + ρg(Deltah) + rhogx = P_"atm" - (2T)/r_2 + rhogx`

⇒ `rhogDeltah = 2T[1/r_1 - 1/r_2]`

⇒ `Deltah = (2T)/(rhog)(1/r_1 - 1/r_2)`

⇒ `Deltah = (2 xx 7.3 xx 10^-2)/(1 xx 10^3 xx 10) (1/((2.5 xx 10^-3)) - 1/((4 xx 10^-3)))`

⇒ `Deltah = 2.19 xx 10^-3`m = 2.19 mm