Question

If Young's modulus of the material is three times of its modulus of rigidity, then its volume elasticity will be

• A. Zero
• B. $3\times 10^{11}N{m}^{-2}$
• C. Infinity
• D. $10.6\times 10^{11}N{m}^{-2}$

Answer 1

Answer: (C)

Since, we know,
$Y=2\eta \left(1+\sigma \right)$ ...(i)
Where, $Y=$ Young's modulus and $\eta =$ modulus of rigidity.
Given, $Y=3\eta$
From Equation (i), we get
$3\eta =2\eta \left(1+\sigma \right)$
$\Rightarrow 1+\sigma =\frac{3}{2}$
$\Rightarrow \sigma =1/2$
$\therefore$ Bulk modulus, $K=\frac{Y}{3(1-2\sigma )}$
Thus, $K=\frac{Y}{3\left(1-2\times \frac{1}{2}\right)}=\frac{Y}{3(1-1)}=\in fty$
Thus, volume elasticity is infinity.