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8.Mechanical Properties of Solids
hard
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 $\left.{Y}=2.0 \times 10^{11} \;{Pa}, {g}=9.8\; {m} / {s}^{2}\right]$
A
$3.60 \times 10^{-8}$
B
$2.60 \times 10^{-7}$
C
$1.87 \times 10^{-3}$
D
$7.07 \times 10^{-4}$
(JEE MAIN-2021)
Solution
Force on each column $=\frac{{mg}}{4}$
$\text { Strain } =\frac{{mg}}{4 {AY}}$
$=\frac{50 \times 10^{3} \times 9.8}{4 \times \pi(1-0.25) \times 2 \times 10^{11}}$
$=2.6 \times 10^{-7}$
Standard 11
Physics
