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physics ncert solutions class 11th Physics Class 11th Mechanical Properties of Solids

9.7 Four identical hollow cylindrical columns of mild steel support a big structure of mass 50,000 kg. The inner and outer radii of each column are 30 and 60 cm respectively. Assuming the load distribution to be uniform, calculate the compressional strain of each column.

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Vishal Baghel | Contributor-Level 10

5 months ago

Mass of the big structure, M = 50000 kg = 50000 $\times 9.8 N$ = 4.9 $\times 10^{5}$ N

Inner radius of the column, r = 30 cm = 0.3 m

Outer radius of the column, R = 60 cm = 0.6 m

Young’s modulus of steel, Y = 2 $\times 10^{11}$ Pa

Total force exerted on 4 columns, F = 4.9 $\times 10^{5}$ N

Force exerted on single column, f = F/4 = 1.225 $\times 10^{5}$ N

Cross sectional area of each column, A = $π (R^{2} - r^{2})$ = $π ({0.6}^{2} - {0.3}^{2})$ = 0.848 $m^{2}$

Stress in each column = f/A

Young’s modulus, Y = Stress / Strain, Strain = Stress / Y = f/ (A $\times Y)$ = $\frac{1.225 \times 10^{5}}{0.848 \times 2 \times 10^{11}} = 7.22 \times 10^{- 7}$ m

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9.7 Four identical hollow cylindrical columns of mild steel support a big structure of mass 50,000 kg. The inner and outer radii of each column are 30 and 60 cm respectively. Assuming the load distribution to be uniform, calculate the compressional strain of each column.

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