A steel girder can bear a load of 25 tonnes. If the depth of the … - Vidyadip

Question

A steel girder can bear a load of 25 tonnes. If the depth of the girdes is doubled, how much load can it bear?

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Answer

If a girder can bear $F _1$ load at depth $d_1$ and $F _2$ load at depth $d_2$, then
$\frac{F_2}{F_1}=\frac{d_2^3}{d_1^3}$
In question, $F _1=25$ tonnes, $d_2=2 d_1$
$\begin{array}{l}
\frac{F_2}{25}=\frac{\left(2 d_1\right)^3}{\left(d_1\right)^3} \\\frac{F_2}{25}=\frac{8 d_1^3}{d_1^3}=8 \\F_2=25 \times 8=200 \text { tonnes }\end{array}$

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