Question

A Steel wire of 20 mm diameter is bent into a circular shapes of 10 m radius. If the modulus of elasticity is $2\times {10}^{6}kg/c{m}^2$ , then the maximum stress induced in the wire is

• A. ${10}^{3}kg\times c{m}^2$
• B. $2\times {10}^{3}kg/c{m}^2$
• C. $4\times {10}^{3}kg/c{m}^2$
• D. $6\times {10}^{3}kg/c{m}^2$

Answer 1

The correct option is B $2\times {10}^{3}kg/c{m}^2$

Using bending formula

$\frac{E}{R}=\frac{M}{I}=\frac{f}{y}$

Given, d = 20 mm

$So,y_{max}=\frac{d}{2}=10mm$

$R=10m=10,000mm$

$E=2\times {10}^{6}kg/c{m}^2$

$f_{max}=\frac{2\times {10}^6\times 10}{10,000}=2\times {10}^{3}kg/c{m}^2$