Question

Young's modulus experiment is performed on a steel wire of $1 \,m$ length and $8\, mm$ diameter. The mass required to be added in the experiment to produce $5\, mm$ elongation of the wire is $\left(Y_{\text {steel }}=2 \times 10^{9} Nm ^{-2}, g=10 m / s ^{2}\right)$

• A. 25 kg
• B. 50 kg
• C. 250 kg
• D. 500 kg

Answer 1

Answer: (B)

Given, $L =1 \,m , r=\frac{a}{2}=4 \,mm =4 \times 10^{-3} \,m$
$\Delta l =5 \,mm =5 \times 10^{-3} \,m $
$Y =\frac{m g L}{\pi r^{2} \Delta l} $
$\Rightarrow \,m=\frac{Y \pi r^{2} \Delta l}{g L} $
$= \frac{2 \times 10^{9} \times 3.14 \times\left(4 \times 10^{-3}\right)^{2} \times\left(5 \times 10^{-3}\right)}{10 \times 1} $
$=\frac{2 \times 3.14 \times 16 \times 5}{10}$
$=50.24 kg \approx 50\, kg$