Question

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 $Y =2.0 \times 10^{11} Pa , g =9.8 \,m / s ^{2}$ ]

• A. $3.60 \times 10^{-8}$
• B. $2.60 \times 10^{-7}$
• C. $1.87 \times 10^{-3}$
• D. $7.07 \times 10^{-4}$

Answer 1

Answer: (B)

Force on each column $=\frac{ mg }{4}$
Strain$=\frac{ mg }{4 AY } $
$=\frac{50 \times 10^{3} \times 9.8}{4 \times \pi(1-0.25) \times 2 \times 10^{11}}$
$=2.6 \times 10^{-7}$