Question

four identical hollow cylindrical columns of steel support a big structure of mass $50000kg$. the inner and outer radius of each column are $30cm$ and $40cm$ respectively. assuming the load distribution to be uniform, calculate the compressional strain of each column.(The young's modulus of steel is $2.0\times {10}^{11}$ Pa)

• A. $2\times {10}^{-5}$
• B. $2.8\times {10}^{-6}$
• C. $5\times {10}^{-4}$
• D. $8\times {10}^{-7}$

Answer 1

The correct option is B $2.8\times {10}^{-6}$

$\begin{array}{cc}\text{Given, weight}=50000Kg& \\ \text{area of cylinders}& =\pi (1600-900)\times {10}^{-4}\\ \text{Force on each cylinder}& =\frac{50000\times 10}{4}\\ & =125000N\end{array}$

$\begin{array}{cc}\text{Now ,}& F=YA\left(\frac{\Delta L}{L}\right)\\ & \Rightarrow \frac{\Delta L}{L}=\frac{125000}{\pi \times 700\times {10}^{-4}\times 2\times {10}^{11}}=2.8\times {10}^{-6}\end{array}$