Question

If the strain in wire is not more than ${10}^{-3}$ and Y = 4 x ${10}^{11}N/m^2$, diameter of wire is 1 mm, then the maximum weight that can be hanged from wire is then:-

• A. $157N$
• B. $314N$
• C. $120N$
• D. $160N$

Answer 1

The correct option is B $314N$

Let the maximum hanged weight be W

So stress produced in this case will be:

$\frac{Force}{Area}=\frac{W}{A}=\frac{W}{\pi {(\frac{1}{2}\times {10}^{-3}m)}^2}=\frac{4W\times {10}^6}{\pi }\to \left(1\right)$ (As diameter $=1$mm)

Max strain in given by:

$\frac{\Delta l}{l}={10}^{-3}\to \left(2\right)$ (given)

So Young's modulus of the wire will have the form:

$Y=\frac{Stress}{Strain}\times 4\times {10}^{11}N/m^2$

$\Rightarrow \frac{4W\times {10}^6}{\pi \times {10}^{-3}}=4\times {10}^{11}N/m^2$

$\Rightarrow W=\pi \times {10}^{2}N=3.14\times {10}^2$

$\Rightarrow W=314N$.