Question

Four identical hollow cylindrical columns, support a big structure of mass M. The inner and another 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

(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. $\frac{Mg}{\pi(R_{1}^{2} - R_{2}^{2})Y}$
• D. $\frac{Mg}{4\pi(R_{1}^{2} - R_{2}^{2})Y}$

Answer 1

Answer: (B)

$\frac{Mg}{4\pi(R_{2}^{2} - R_{1}^{2})Y}$

Answer 2

: 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

$= \frac{F}{AY} = \frac{Mg}{4\pi(R_{2}^{2} - R_{1}^{2})Y}$