Four identical hollow cylindrical columns of mild steel support a big structure of mass \(50 \times 10^{3} {kg}\), The inner and outer radii of each column are \(50\; {cm}\) and \(100 \;{cm}\) respectively. Assuming uniform local distribution, calculate the compression strain of each column. [Use \(\left.{Y}=2.0 \times 10^{11} \;{Pa}, {g}=9.8\; {m} / {s}^{2}\right]\)

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Correct Answer

(B) \(2.60 \times 10^{-7}\)

Step-by-step Solution

Detailed explanation

Force on each column \(=\frac{{mg}}{4}\)

\(\text { Strain } =\frac{{mg}}{4 {AY}}\)

\(=\frac{50 \times 10^{3} \times 9.8}{4 \times \pi(1-0.25) \times 2 \times 10^{11}}\)

\(=2.6 \times 10^{-7}\)

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