Answer:
the bar was stretched by [tex]\mathbf{\Delta L = 3.36 \ mm}[/tex]
the length of the after it was stretched is [tex]\mathbf{L_{new} = 603.36 \ mm}[/tex]
Explanation:
From the information given:
The strain gauge resistance R = 250 Ω
The gauge factor = 1
The original length L = 0.6 m = 600 mm
After the bar is being stretched under tension force;
the new resistance [tex]R_{new} = 251.42[/tex]
The gauge factor [tex]G = \dfrac{\Delta R/R}{\Delta L /L }[/tex]
where;
[tex]\Delta R = R_{new} - R[/tex] and [tex]\Delta L = L_{new} - L[/tex]
ΔR = 251.4 - 250
ΔR = 1.4 Ω
[tex]\Delta L = L_{new} - L[/tex]
[tex]L_{new} = L + L (\dfrac{\Delta R/R}{G})[/tex]
[tex]L_{new} = 0.6 + 0.6 (\dfrac{\Delta 1.4/250}{1})[/tex]
[tex]L_{new} = 0.60336 \ m[/tex]
[tex]\mathbf{L_{new} = 603.36 \ mm}[/tex]
Thus, the length of the after it was stretched is [tex]\mathbf{L_{new} = 603.36 \ mm}[/tex]
Thus, the bar was stretched by [tex]\Delta L = L_{new} - L[/tex]
[tex]\Delta L = (603.36 - 600) \ mm[/tex]
[tex]\mathbf{\Delta L = 3.36 \ mm}[/tex]
