Answer

Verified

382.5k+ views

**Hint:**In physics, thermal conductivity is defined as the measurement of the ability of a material to conduct heat or allow it to pass heat energy. It's denoted by $K$ . We will use the general formula of thermal conductivity to find the ratio of lengths of two rods.

**Complete step-by-step solution:**

We know that the general formula of thermal conductivity is given as:

$K = \dfrac{{Qd}}{{AT}}$ where,

$Q$ Is the amount of heat produced in the rod at given temperature

$d$ Is the length of the rod

$A$ Is the area of the cross section of the rod.

$T$ Is the temperature at which thermal conductivity is measured

$K$ Is called the thermal conductivity of a material.

We have given that the thermal resistances and area of cross section of two rods are same which means the thermal conductivity of both rods depends upon the length only, so

Let ${K_1}$ and ${K_2}$ be the thermal conductivity of two rods and there ratio are given as $\dfrac{{{K_1}}}{{{K_2}}} = \dfrac{5}{4}$

Since, thermal conductivities are directly proportional to lengths of rod so,

$\dfrac{{{K_1}}}{{{K_2}}} = \dfrac{{{d_1}}}{{{d_2}}}$

$\dfrac{{{K_1}}}{{{K_2}}} = \dfrac{5}{4} = \dfrac{{{d_1}}}{{{d_2}}}$

$ \Rightarrow \dfrac{{{d_1}}}{{{d_2}}} = \dfrac{5}{4}$

So, the ratio of length of two rods are $5:4$

**Hence, the correct option is (D).**

**Note:**It should be remembered that, the SI unit of thermal conductivity is $W{m^{ - 1}}{K^{ - 1}}$ and thermal conductivity decreases with increase in area of a body and also decreases with rise in temperature which means body at low temperature allow much heat to pass through them.

Recently Updated Pages

what is the correct chronological order of the following class 10 social science CBSE

Which of the following was not the actual cause for class 10 social science CBSE

Which of the following statements is not correct A class 10 social science CBSE

Which of the following leaders was not present in the class 10 social science CBSE

Garampani Sanctuary is located at A Diphu Assam B Gangtok class 10 social science CBSE

Which one of the following places is not covered by class 10 social science CBSE

Trending doubts

Which places in India experience sunrise first and class 9 social science CBSE

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

How do you graph the function fx 4x class 9 maths CBSE

In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Give 10 examples for herbs , shrubs , climbers , creepers

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Why is there a time difference of about 5 hours between class 10 social science CBSE