Question

Find the maximum load which may be placed on a tungsten wire of diameter $2mm$ so that permitted strain must not exceed $\frac{1}{1000}$.
$(Y_{tungsten}=35\times {10}^{10})$

• A. $4000N$
• B. $1100N$
• C. $200N$
• D. $300N$

Answer 1

The correct option is B $1100N$

Given: Strain $=\frac{1}{1000}={10}^{-3}$,

Young's modulus of elasticity $=Y=35\times {10}^{10}N/m^2$,

Diameter of wire $=2mm$,

Raqdius of wire $=\frac{2}{2}=2mm=10\times {10}^{-3}m$

To Find: Maximum load $=F=?$

$Y=\frac{Stress}{Strian}=\frac{\left(F/A\right)}{Strain}$

$\therefore F=\pi r^2\times Y\times strian$

$\therefore F=3.142\times (1\times {10}^{-3})\times 35\times {10}^{10}\times {10}^{-3}$

$\therefore F=3.142\times 1\times {10}^{-6}\times 35\times {10}^{10}\times {10}^{-3}$

$\therefore F=1100N$

Ans: Maximum load can be placed is $1100N$