First slide

Stress and strain

Question

A steel rod of length 1 m and radius 10 mm is stretched by a force 100 kN along its length. The stress produced in the rod is $Y_{Steel} = 2 \times 10^{11} {Nm}^{- 2}$

Moderate

A

$3 .18 \times 10^{6} {Nm}^{- 2}$
B

$3.18 \times 10^{7} {Nm}^{- 2}$
C

$3.18 \times 10^{8} {Nm}^{- 2}$
D

$3.18 \times 10^{9} {Nm}^{- 2}$

Solution

$Here, r = 10 mm = 10 \times 10^{- 3} = 10^{- 3} m$
$L = 1 m, F = 100 kN = 100 \times 10^{3} N = 10^{5} N$
Stress produced in the rod is
Strain = $\frac{F}{A} = \frac{F}{{πr}^{2}} = \frac{100 \times 10^{3} N}{3 .14 \times {(10^{- 2} m)}^{2}}$
$= 3 .18 \times 10^{8} {Nm}^{- 2}$

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