Correct Answer – Option 1 : 230° C

Concept:

The linear expansion coefficient is an intrinsic property of every material. Hence it varies from one material to another. The rate at which a material expands purely depends on the cohesive force between the atoms. Cohesive force is the force that binds two or more atoms. In other words, the cohesive force resists the separation between the atoms. However, the greater the cohesive force, the expansion will be low for a given increase in temperature.

Thermal expansion in length of rod due to heating is given by the relation.
Δl = l₀ α(ΔT) = l₀ α(T₂ – T₁)

Calculation:

Let initial length of identical rods is l₀

Thermal expansion in length of rod due to heating is given by the relation

Δl = l₀ α(ΔT) = l₀ α(T₂ – T₁ )

Here, α is coefficient of linear expansion.

So, change in length of rods are

Δl₁ = l₀ α₁ (180 – 30)

Δl₂ = b₀ α₂ (T – 30)

Because new lengths are same, so change in lengths of both rods are equal.

i.e. Δl₁ = Δl₂

⇒ l₀ α₁ (180 – 30) = l₀ α₂ (T – 30)

\({\rm{or\;}}\frac{{{\alpha _1}}}{{{\alpha _2}}} = \frac{{\left( {T – 30} \right)}}{{150}}\) 

Given α₁ : α₂ = 4 : 3

\(\therefore \;\frac{{T – 30}}{{150}} = \frac{4}{3} \Rightarrow T – 30 = \frac{4}{3} \times 150 = 200\)

or T = 200 + 30 = 230°C