Question

The adjacent graph shows the extension $(\Delta \ell)$ of a wire of length 1 m suspended from the top of a roof at one end with a load w connected to the other end. If the crosssectional area of the wire is $10^{-6} m^2$, what is Young’s modulus of the wire?

• A. $2 \times 10^{11} Nm ^{-2}$
• B. $2 \times 10^{-11} Nm ^{-2}$
• C. $\times 10^{-12} Nm ^{-2}$
• D. $2 \times 10^{-14} Nm ^{-2}$

Answer 1

Answer: (A)

From the graph, $\ell=10^{-4} m , F =20 \,N$
$\ell=1 \times 10^{-4} \,m$
Given: $A =10^{-6} m ^{2}, L =1\, m$
$\therefore Y=\frac{F L}{A \ell}$
$=\frac{20 \times 1}{10^{-6} \times 10^{-4}}$
$=20 \times 10^{10}$
$=2 \times 10^{11} Nm ^{-2}$