Question

A load of $4.0 \,kg$ is suspended from a ceiling through a steel wire of length $2.0 \,m$ and radius $2.0 \,mm$. It is found that the length of the wire increases by $0.031\, mm$ as equilibrium is achieved. Taking, $g=3.1 \,\pi ms ^{-2}$, the Young's modulus of steel is

• A. $2.0 \times 10^{8} Nm ^{-2}$
• B. $2.0 \times 10^{9} Nm ^{-2}$
• C. $2.0 \times 10^{11} Nm ^{-2}$
• D. $2.0 \times 10^{13} Nm ^{-2}$

Answer 1

Answer: (C)

As, $Y=\frac{M g L}{\pi r^{2} \times l}=\frac{4 \times(3.1 \pi) \times(2.0)}{ \left.\pi \times\left(2 \times 10^{-3}\right)^{2} \times 0.031 \times 10^{-3}\right)}$
$=2 \times 10^{11} Nm ^{-2}$