Question

A load of $4.0kg$ is suspended from a ceiling through a steel wire of length $20m$ and radius $2.0mm$. It is found that the length of the wire increases by $0.031mm$ as equilibrium is achieved. If $g=3.1x\pi m{s}^{-2}$, the value of young's modulus in $N{m}^{-2}$ is

• A. $2.0\times {10}^{12}$
• B. $4.0\times {10}^{11}$
• C. $2.0\times {10}^{11}$
• D. $0.02\times {10}^9$

Answer 1

The correct option is A $2.0\times {10}^{12}$

For equilibrium
Weight = Tension
$mg=T$
$\therefore T=4\times 3.1\pi$$=12.4\pi N$ (as can be inferred from the question)
$Y=\frac{T/A}{△l/l}$
$=\frac{12.4\pi /\pi (\frac{2}{1000}{)}^2}{\frac{0.031}{1000}/20}$
$=\frac{12.4\times 20\times 1000\times (1000{)}^2}{4\times 0.031}$
$=2\times {10}^{12}N/m^2$