Question

u tube with liquid filled inside if the the system is at rest then the value of h will be density of oil 0.8 mercury 13.6 glycerine 1.3​

Answer 1

The length of oil column is 9.6 cm

Explanation:

Correct statement:

A vertical u tube of uniform cross section contains mercury in both sides.a glycerine ( density 1.3 g/c.c) column of 10 cm is introduced into one arm.Oil of density 0.8 g/c.c is poured into the other arm until the oil and glycerine are in the same horizontal level; Find the length of oil column. density of mercury= 13.6 g/c.c

Solution:

Let length of oil column is L.

We can write:

Pressure due to oil + pressure due to mercury = pressure due to glycerine

ρoilgL + ρHg x g (10 - L) = ρ.gly.g10

Given, density of oil = 0.8 g/cm³

Density of mercury = 13.6 g/cm³

Density of glycerine = 1.3 g/cm³

So, 0.8 × L + 13.6 (10 - L) = 1.3 × 10

0.8 L + 136 - 13.6 L = 13

12.8 L = 123

L = 9.6 cm

Hence, length of oil column = 9.6 cm

Also learn more

A beam 9 m long, 50 cm wide, and 20 cm deep is made of wood which weights 30 kg per cubic metre. find the weight of the beam ?

https://brainly.in/question/1170092

Answer 2

Complete question:

A vertical U-tube of uniform cross-section contains mercury in both sides of its arms as shown below. Gylcerine column of  10 cm is introduced into one of its arms. Oil of density 0.8 g/cc is poured into the other arm until the upper surface of the oil and glycerine are at same horizontal level. The length of oil column is [Density of Hg = 13.6 cc/g and density of glycerine = 1.3 g/cc].

Answer:

The length of oil column is 9.6 cm

The image given in question is attached below.

Given:

Height of glycerine column = 10 cm

Density of oil = 0.8 g/cc

Density of Hg = 13.6 cc/g

Density of glycerine = 1.3 g/cc

Explanation:

Let x be the height of oil column.

From image, pressure excreted by glycerine is equal to pressure excreted by oil and mercury.

Pressure from glycerine = Pressure from oil + Pressure from mercury

Pressure = Density × g × Height of column

Pressure from glycerine = Density of glycerine × g × Height of glycerine column

∴ Pressure from glycerine = 1.3 × g × 10

Pressure from oil = Density of oil × g × Height of oil column

∴ Pressure from oil = 0.8 × g × x

Pressure from mercury = Density of mercury × g × Height of mercury column

∴ Pressure from mercury = 13.6 × g × (10 - x)

Now,

1.3 × g × 10 = (0.8 × g × x) + (13.6 × g × (10 - x))

1.3 × 10 = (0.8 × x) + (13.6 × (10 - x))

13 = 0.8x + 136 - 13.6x

13 = - 12.8x + 136

12.8x = 136 - 13 ⇒ 12.8x = 123

∴ x = 123/12.8 = 9.6 cm