Question

$Y,K,\eta$ represent respectively the youngs modulus,bulk modulus and rigidity modulus of a body. If rigidity modulus is twice the bulk modulus, then

• A. $Y=5K/18$
• B. $Y=5\eta /9$
• C. $Y=9K/5$
• D. $Y=18K/5$

Answer 1

The correct option is D $Y=18K/5$

$\begin{array}{c}\text{Given, young's modulus}=Y\\ \text{bulk modulus}=K\\ \text{modulus of rigidity}=\eta \\ \text{We know that,}\begin{array}{c}Y=3k(1-2\sigma )\\ Y=2n(1+\sigma )\end{array}\\ \text{where}\sigma \text{is the stress applied.}\end{array}$

$\begin{array}{c}\text{Now, on eliminating}\\ \sigma \text{from above equations, we get}\\ Y=\frac{9nk}{\eta +3k}\end{array}$

$\begin{array}{c}\text{Given,}\eta =2K\\ \therefore Y=\frac{18K}{5}\\ \text{Hence, option}D\text{is the correct answer.}\end{array}$