Question

Diameter of two limbs of a u tube are 2mm and 5mm and surface tension is 70 dyne/cm, if water density is 1000 kg/m3 and g = 10 m/s2 then water level difference in both the tubes will be

Answer 1

Answer:

The difference between the water level in both tubes is 4.2 meters

Explanation:

Given as :

Measure of water density = $\rho$ =  1000 kg/$m^{3}$

Radius of limbs = $r_1$ = 2 mm

Or , $r_1$= 2 × $10^{-3}$ m

And

$r_2$ = 5 mm

Or, $r_2$ = 5 × $10^{-3}$ m  

Surface tension = T = 70 dyne/cm

or, T = 0.07 N/m

Let The height of water level in tube 1 = $h_1$ meters

And The height of water level in tube 2 = $h_2$  meters

Let The difference between the water level = H  meters

According to question

Difference in height  = $\dfrac{2T}{g}$ × ( $\dfrac{1}{r_1}$  -  $\dfrac{1}{r_2}$  )

Or, H  = $\dfrac{2\times 0.07}{10}$ × ( $\dfrac{1}{2\times 10^{-3}}$  -  $\dfrac{1}{5\times 10^{-3}}$  )

Or, H = 0.014 × ( 500  -  200 )

Or, H = 0.014 × 300

∴   H = 4.2 m

So, The difference between the water level = H = 4.2 meters

Hence, The difference between the water level is 4.2 meters  Answer