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Answer :
Answer:13.33 tons
Explanation:
Given
Weight of a material varies as
[tex]W\propto b[/tex] (width)
[tex]W\propto h^2[/tex] (height)
[tex]W\propto \frac{1}{L}[/tex] (length)
[tex]W=k\frac{bh^2}{L}[/tex]
Dimension of first beam
[tex]b=\frac{1}{3}[/tex] foot
[tex]h=\frac{1}{2}[/tex] foot
[tex]L=15[/tex] foot
Weight supported [tex]W=20 tons[/tex]
Second beam
[tex]b=\frac{1}{2} foot[/tex]
[tex]h=\frac{1}{3} foot[/tex]
[tex]h=15 feet[/tex]
let weight of second beam be [tex]W_2[/tex]
taking both beams at the same time
[tex]\frac{20}{W_2}=\frac{\frac{1}{3}\times (\frac{1}{2})^2}{15}\times \frac{15}{\frac{1}{2}\times (\frac{1}{3})^2}[/tex]
[tex]\frac{20}{W_2}=\frac{3}{2}[/tex]
[tex]W_2=\frac{40}{3} \approx 13.33 tons[/tex]
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