Question

If the longitudinal strain in a cubical body is three times the lateral strain then the bulk modulus $K$, Young's modulus $Y$ and rigidity modulus $G$ are related by

• A. $K=3Y$
• B. $G=\frac{Y}{8}$
• C. $G=\frac{3Y}{8}$
• D. $G=\frac{Y}{4}$

Answer 1

The correct option is C $G=\frac{3Y}{8}$

Given that longitudinal strain in a cubical body is three times the lateral strain,
Hence $\mu =\frac{1}{3}$

Relations between modulii of elasticity and poissons ratio is
$Y=2G(1+\mu )$
$\mu =\frac{Y}{2G}-1$
$\frac{Y}{2G}=\frac{1}{3}+1$
$G=\frac{3Y}{8}$