Consider a rod stell having radius of 8 mm and the length of 2 m. If a force of 150 kN stretches it along its length, then calculate the stress and strain in the rod, if the elongation in length is 7.46 mm.

Options

A. `7.46 xx 10^(8) N,^(-2)` and `3.73 xx 10^(-3)`
B. `7.43 xx 10^(6) Nm^(-2)` and `2.73 xx 10^(-5)`
C. `7.28 xx 10^(10) Nm^(-2)` and `2.83 xx 10^(-4)`
D. None of the above

Explanation

If the rod stretches along it length, then the stress produced is the tensile stress whereas the strain produced is longitudinal strain.
Given, radius, `r = 8 mm = 8 xx 10^(-3) m`, length, `L = 2m`
Force, `F = 150 kN = 15 xx 10^(4) N`
Area, `A = pi r^(2) = pi xx (8 xx 10^(-3))^(2) = 201 xx 10^(-6) m^(2)`
Increase in length, `Delta L = 7.4 mm = 7.46 xx 10^(-3) Nm^(-2)`
stress and strain = ?
Stress `= (F)/(A) = (15 xx 10^(4))/(201 xx 10^(8)) = 0.0746 xx 10^(10) Nm^(-2)`
`= 7.46 xx 10^(8) Nm^(-2)`
Longitudinal strain `= (Delta L)/(L) = (7.46 xx 10^(-3))/(2) = 3.73 xx 10^(-3)`