Question

A glass rod of radius 1 mm is inserted symmetrically into a glass capillary tube with inside radius 2 mm. Then the whole arrangement is brought in contact of the surface of water. Surface tension of water is 7×10−2n/m. To what height will the water rise in the capillary?(θ=0∘)a glass rod of radius 1 mm is inserted symmetrically into a glass capillary tube with inside radius 2 mm. Then the whole arrangement is brought in contact of the surface of water. Surface tension of water is 7×10−2n/m. To what height will the water rise in the capillary?(θ=0∘)a glass rod of radius 1 mm is inserted symmetrically into a glass capillary tube with inside radius 2 mm. Then the whole arrangement is brought in contact of the surface of water. Surface tension of water is 7×10−2n/m. To what height will the water rise in the capillary?(θ=0∘)

Answer 1

Total upward Force due to surface Tension ,

F= T ( 2πr 1 + 2πr2)-> (1)

where T is surface tension of water=7×10 -2N /m

r1 is radius of the glass rod =1mm

r2 is the radius of the capillary tube=2mm

Weight of the liquid Column, W=h [πr2 2 − πr1 2 ]dg->(2)

Now on equating (1) and (2) equations ,

we get , hπ (r1 + r2)(r2 − r1)dg = 2Tπ( r1 + r2)

where d is density of the water = 10 kg/ 3

m3 g is the acceleration due to gravity = 10 m/s 2

So h = 2T (r2−r1)dg

= 2×7×10 -2 (2−1)×10−3×10×10 3

= 14 × 10−3m

= 1. 4 × 10−2m

= 1. 4 cm

Answer 2

Given:

Radius = 1 mm

Inside radius = 2 m

Surface tension = 7 * 10^-2 n/m

To find:

The rise of water in the capillary.

Solution:

To find the rise of water,

The total upward force is calculated,

Force = T ( 2 π r1 + 2 π r2)

Where,

T - surface tension

r1 - radius of the glass rod

r2 - radius of the capillary tube

By formula,

Weight of the liquid Column, W = h [ ( π r2 )^2 − ( π r1 )^2 ]dg

Equating,

We get,

h π ( r1 + r2 ) ( r2 − r1 ) dg = 2 T π ( r1 + r2 )

Where,

d - density of the water

d = 10 kg / m^3

g - acceleration due to gravity

g = 10 m / s^2

So,

Height = 2 T ( r2 − r1 ) dg

2 * 7 * ( 10 -2 ( 2 − 1 ) ) * 10 − 3 × 10 × 10

1. 4 × 10−2m

Height = 1. 4 cm

Hence, the water rise in the capillary will rise up to 1.4 cm.