Answer:
Both rod have the same tensile stress
Explanation:
Given information,
The weight first rod, [tex]W_{1}[/tex] = 1000 N
The length of first rod, [tex]l_{1}[/tex] = 2.0 m
The weight second rod, [tex]W_{2}[/tex] = 500 N
The length of second rod, [tex]l_{2[/tex] = 1.0 m
The equation of tensile stress, σ = [tex]\frac{F}{A}[/tex]
where
σ = tensile stress (N/[tex]m^{2}[/tex] or Pa)
F = Force (N)
A = Area (N/[tex]m^{2}[/tex] or Pa)
so
σ1 = [tex]\frac{W_{1} }{A_{1} }[/tex], A = 2πl
= [tex]\frac{1000}{2\pi(2) }[/tex]
= [tex]\frac{250}{\pi }[/tex] N/[tex]m^{2}[/tex]
now calculate σ2
σ2 = [tex]\frac{W_{2} }{A_{2} }[/tex]
= [tex]\frac{500}{2\pi(1) }[/tex]
= [tex]\frac{250}{\pi }[/tex] N/[tex]m^{2}[/tex]
σ1/σ2 = [tex]\frac{250}{\pi }[/tex] / [tex]\frac{250}{\pi }[/tex]
σ1/σ2 = 1
σ1 = σ2
Hence, the tensile stress of first and second rod are the same.
