Question

A block of mass $3\text{kg}$ produces an extension of $1\text{mm}$ in a wire of length $4\text{m}$ and diameter $4\text{mm}$ when suspended at one end. The Young's modulus of the material of the wire will be (Assume: $g=10{\text{m/s}}^2\text{and}\pi =3$)

• A. ${10}^{10}{\text{N/m}}^2$
• B. $4\times {10}^{10}{\text{N/m}}^2$
• C. $3\times {10}^{10}{\text{N/m}}^2$
• D. $5.88\times {10}^{10}{\text{N/m}}^2$

Answer 1

The correct option is A ${10}^{10}{\text{N/m}}^2$

Young modulus is given by $\left(Y\right)=\frac{FL}{A\Delta L}$

where $F=$ Force
$L=$ length
$\Delta L=$ change in length
$A=$ Area of cross section

$F=mg=3\times 10=30\text{N}$
$L=4\text{m}$
$\Delta L=1\times {10}^{-3}\text{m}$
$A=\frac{\pi }{4}(\text{diameter}{)}^2=\frac{\pi }{4}(4\times {10}^{-3}{)}^2$
$=12\times {10}^{-6}{\text{m}}^2$

Substituting the values
$\therefore Y=\frac{30\times 4}{(12\times {10}^{-6})\times {10}^{-3}}{\text{N/m}}^2$
$={10}^{10}{\text{N/m}}^2$