Question

The ratio of the lengths of two rods is 4: 3. The ratio of their coefficients of cubical expansion is 2: 3.Then the ratio of their linear expansion when they are heated through same temperature difference is x : 9. then x value ___________

Answer 1

Answer:

x = 8

Explanation:

Given :

• The ratio of the lengths of two rods is 4 : 3.
• The ratio of their coefficients of cubical expansion is 2 : 3.
• The ratio of their linear expansion when they are heated through same temperature difference is x : 9.

To find :

the value of x

Solution :

The relation between coefficient of cubical expansion and coefficient of linear expansion is given as,

γ = 3α

where

γ denotes the coefficient of cubical expansion

α denotes the coefficient of linear expansion

As given,

γ₁ : γ₂ = 2 : 3

Then, the ratio of the coefficients of linear expansion is

α₁ : α₂ = γ₁/3 : γ₂/3

= γ₁ : γ₂

= 2 : 3

The linear expansion is given by,

∆l = lα∆T

where

l denotes the initial length

α denotes the coefficient of linear expansion

∆T denotes the change in temperature

Let l₁ and l₂ be the lengths of the two rods.

l₁ : l₂ = 4 : 3

$\tt \dfrac{\triangle l_1}{\triangle l_2} = \dfrac{l_1 \alpha _1 \triangle T}{l_2 \alpha _2 \triangle T} \\\\ \tt \dfrac{x}{9} = \dfrac{4}{3} \times \dfrac{2}{3} \\\\ \tt \dfrac{x}{9} = \dfrac{8}{9} \\\\ \longrightarrow \tt x=8$

The value of x is 8

Answer 2

Answer:

8

Explanation: