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, $K=\frac{Y}{3 \left(\right. 1 - 2 \sigma \left.\right)}$
Thus, $K=\frac{Y}{3 \left(1 - 2 \times \frac{1}{2}\right)}=\frac{Y}{3 \left(\right. 1 - 1 \left.\right)}=\in fty$
Thus, volume elasticity is infinity.