At 20^∘ C, a steel ruler of 20 cm long is graduated to give correct reading, but when it is use

Name: Problem 13, Chapter 15: Arihant AIEEE Physics
Uploaded: 2021-09-19T14:40:40-08:00
Duration: 1 min 25 s
Channel: Ajay Singhal
Description: At 20^∘ C, a steel ruler of 20 cm long is graduated to give correct reading, but when it is used at a temperature of 40^∘ C, what will be the actual length of the steel ruler? [αstèel =1.2 ×10^-5( ^∘ C)^-1] (a) 22.02 cm (b) 19.6 cm (c) 20.0048 cm (d) 18.0002 cm

step 1 Hello students in this question we have a temperature T1 equals to 20 degrees centigrade at whic

Question

At $20^{\circ} \mathrm{C}$, a steel ruler of $20 \mathrm{~cm}$ long is graduated to give correct reading, but when it is used at a temperature of $40^{\circ} \mathrm{C}$, what will be the actual length of the steel ruler? $\left[\alpha_{\text {stèel }}=1.2 \times 10^{-5}\left({ }^{\circ} \mathrm{C}\right)^{-1}\right]$ (a) $22.02 \mathrm{~cm}$ (b) $19.6 \mathrm{~cm}$ (c) $20.0048 \mathrm{~cm}$ (d) $18.0002 \mathrm{~cm}$

   At $20^{\circ} \mathrm{C}$, a steel ruler of $20 \mathrm{~cm}$ long is graduated to give correct reading, but when it is used at a temperature of $40^{\circ} \mathrm{C}$, what will be the actual length of the steel ruler? $\left[\alpha_{\text {stèel }}=1.2 \times 10^{-5}\left({ }^{\circ} \mathrm{C}\right)^{-1}\right]$
(a) $22.02 \mathrm{~cm}$
(b) $19.6 \mathrm{~cm}$
(c) $20.0048 \mathrm{~cm}$
(d) $18.0002 \mathrm{~cm}$

Arihant AIEEE Physics

D.B. Singh 2006 Edition

Chapter 15, Problem 13

Instant Answer

Solved by Expert Ajay Singhal

09/19/2021

Step 1

The ruler gives correct readings at this temperature. Show more…

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At $20^{\circ} \mathrm{C}$, a steel ruler of $20 \mathrm{~cm}$ long is graduated to give correct reading, but when it is used at a temperature of $40^{\circ} \mathrm{C}$, what will be the actual length of the steel ruler? $\left[\alpha_{\text {stèel }}=1.2 \times 10^{-5}\left({ }^{\circ} \mathrm{C}\right)^{-1}\right]$ (a) $22.02 \mathrm{~cm}$ (b) $19.6 \mathrm{~cm}$ (c) $20.0048 \mathrm{~cm}$ (d) $18.0002 \mathrm{~cm}$

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Key Concepts

Thermal Expansion

Thermal expansion is the tendency of matter to change its dimensions—length, area, or volume—when subjected to a change in temperature. This phenomenon occurs because the kinetic energy of atoms or molecules increases with temperature, causing them to move apart and thus leading to an expansion of the material.

Linear Thermal Expansion Coefficient

The linear thermal expansion coefficient is a material-specific constant that quantifies the fractional change in length per degree change in temperature. It is used in the linear expansion formula, ?L = L???T, where ?L is the change in length, L? is the original length, ? is the coefficient, and ?T is the temperature change. This concept is crucial for predicting dimensional changes in materials, such as rulers, under temperature variations.

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