Question:
Four identical hollow cylindrical columns of mild steel support a big structure of mass $50 \times 10^{3} \mathrm{~kg}$, The inner and outer radii of each column are $50 \mathrm{~cm}$ and $100 \mathrm{~cm}$ respectively. Assuming uniform local distribution, calculate the compression strain of each column. [Use $\mathrm{Y}=2.0 \times 10^{11} \mathrm{~Pa}, \mathrm{~g}=9.8 \mathrm{~m} / \mathrm{s}^{2}$ ]
Correct Option: , 2
Solution:
Force on each column $=\frac{\mathrm{mg}}{4}$
Strain $=\frac{\mathrm{mg}}{4 \mathrm{AY}}$
$=\frac{50 \times 10^{3} \times 9.8}{4 \times \pi(1-0.25) \times 2 \times 10^{11}}$
$=2.6 \times 10^{-7}$