Question

Four identical hollow cylindrical columns, support a big structure of mass $M$. The inner and outer radii of a column are $R_1$ and $R_2$ respectively. Assuming the load distribution to be uniform, the compressional strain of each column is then
(where $Y$ is Young's modulus of the column )

• A. $\frac{Mg}{\pi (R_2^2-R_1^2)Y}$
• B. $\frac{Mg}{4\pi (R_2^2-R_1^2)Y}$
• C. $\frac{Mg}{5\pi (R_1^2-R_2^2)Y}$
• D. $\frac{Mg}{6\pi (R_1^2-R_2^2)Y}$

Answer 1

The correct option is B $\frac{Mg}{4\pi (R_2^2-R_1^2)Y}$

Area of cross-section of each column, $A=\pi (R_2^2-R_1^2)$
Since each column supports one-quarter of the load
$\therefore F=\frac{Mg}{4}$
Compressional strain of each column $=\frac{F}{AY}=\frac{Mg}{4\pi (R_2^2-R_1^2)Y}$