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Chapter 7: Problem 940

For a given material the Young's modulus is \(2.4\) times that of rigidity modulus. What is its poisson's ratio? (A) \(2.4\) (B) \(1.2\) (C) \(0.4\) (D) \(0.2\)

Short Answer

Expert verified
The Poisson's ratio for the given material is \(0.2\), which corresponds to the answer (D).

Step by step solution

01

Write down the given values.

We are given that Young's modulus (E) is 2.4 times the rigidity modulus (G). So, we can write this relationship as: \(E = 2.4G\)
02

Substitute the given relationship into the formula.

Now we substitute the relationship between E and G into the formula relating Young's modulus, rigidity modulus, and Poisson's ratio: \(2.4G = 2G (1 + ν)\)
03

Solve for Poisson's ratio.

To find the Poisson's ratio (ν), we need to solve the equation obtained in step 2. Divide both sides of the equation by 2G: \(1.2 = 1 + ν\) Now, subtract 1 from both sides of the equation: \(ν = 1.2 - 1\) So, \(ν = 0.2\) The Poisson's ratio for the given material is 0.2, which corresponds to the answer (D).

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