Question

Two steel wires having same length are suspended from a ceiling under the same load. If the ratio of their energy stored per unit volume is $1:4$, the ratio of their diameters is :

• A. $1:2$
• B. $\sqrt{2}:1$
• C. $2:1$
• D. $1:\sqrt{2}$

Answer 1

Answer: (B)

$\frac{Energystored}{Volume}=\frac{1}{2}\frac{{\left(Stress\right)}^2}{Y}$
$\frac{u_1}{u_2}=\frac{1}{4}\Rightarrow 4u_1=u_2$
$4\frac{1}{2Y}{\left[\frac{W\cdot 4}{\pi d_1^2}\right]}^2=\frac{1}{2Y}{\left[\frac{W\cdot 4}{\pi d_2^2}\right]}^2$
$4={\left(\frac{d_1}{d_2}\right)}^4$
$\Rightarrow \frac{d_1}{d_2}=\sqrt{2}:1$