Question

A block of mass $4\mathrm{Kg}$ is suspended from the ceiling with the help of a steel wire off radius $2\mathrm{mm}$ and negligible mass. Find the stress in the wire ($\mathrm{g}={\mathrm{\pi }}^2$)

• A. $4\times {10}^6{\mathrm{Nm}}^{-2}$
• B. $3\times {10}^5{\mathrm{Nm}}^{-2}$
• C. $3.14\times {10}^6{\mathrm{Nm}}^{-2}$
• D. $2\times {10}^6{\mathrm{Nm}}^{-2}$

Answer 1

The correct option is C

$3.14\times {10}^6{\mathrm{Nm}}^{-2}$

Step 1: Given data

Mass of block $\mathrm{m}=4\mathrm{Kg}$

Radius of steel wire $\mathrm{r}=2\mathrm{mm}=0.002\mathrm{m}$

Acceleration due to gravity $\mathrm{g}={\mathrm{\pi }}^2$

Step 2: Finding the stress in the wire

The force per unit area is known as stress. Mathematically it is written as:

$\mathrm{Stress}=\frac{\mathrm{Force}}{\mathrm{Area}}=\frac{\mathrm{mg}}{\mathrm{A}}$

Its unit is ${\mathrm{Nm}}^{-2}$. Now calculating the stress in a wire, we have

$\mathrm{Stress}=\frac{\mathrm{Force}}{\mathrm{Area}}=\frac{\mathrm{mg}}{{\mathrm{\pi r}}^2}=\frac{4\times {\mathrm{\pi }}^2}{\mathrm{\pi }\times {(0.002)}^2}=\frac{4\mathrm{\pi }}{{(0.002)}^2}=3.14\times {10}^6{\mathrm{Nm}}^{-2}$

Hence, option(C) is the correct answer.