/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 39 Two rods of length \(L_{1}\) and... [FREE SOLUTION] | 91影视

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Chapter 10: Problem 39

Two rods of length \(L_{1}\) and \(L_{2}\) are made of materials whose coefficients of linear expansion are \(\alpha_{1}\) and \(\alpha_{2}\). If the difference between the two lengths is independent of temperature. (A) \(\left(L_{1} / L_{2}\right)=\left(\alpha_{1} / \alpha_{2}\right)\) (B) \(\left(L_{1} / L_{2}\right)=\left(\alpha_{2} / \alpha_{1}\right)\) (C) \(L_{1}^{2} \alpha_{1}=L_{2}^{2} \alpha_{2}\) (D) \(\alpha_{1}^{2} L_{1}=\alpha_{2}^{2} L_{2}\)

Short Answer

Expert verified
The answer is (B) \(L1/L2 = 伪2/伪1\). This is the condition that ensures the difference between the lengths of the two rods remains constant regardless of the temperature change.

Step by step solution

01

Understanding the Concept

The length \( 螖L \) of an object under a temperature change \( 螖T \) is given by the formula \( 螖L = 伪L_0螖T \), where \( 伪 \) is the coefficient of linear expansion and \( L_0 \) is the initial length of the rod. As per the problem, the change in length of both rods is the same.
02

Formulate the Equations

Apply the formula for the change in length due to temperature for both rods. We have \( 螖L1 = 伪1L1螖T \) and \( 螖L2 = 伪2L2螖T \). As it's specified in the problem that the change in lengths stays the same across temperatures, we can equate these two expressions. This leads to \( 伪1L1螖T = 伪2L2螖T \).
03

Simplify the Equation

Solving the equation \( 伪1L1螖T = 伪2L2螖T \), we can cancel the \( 螖T \) from both sides since it's common to both. It leads us to \( 伪1L1 = 伪2L2 \). If we rearrange this to get \( L1/L2 \), it gives us \( L1/L2 = 伪2/伪1 \).

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Most popular questions from this chapter

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