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Statement for Linked Answer Questions 76 and 77: A cylindrical container of radius \(R = 1\,\text{m}\), wall thickness 1 mm, is filled with water up to a depth of 2 m and suspended along its upper rim. The density of water is 1000 kg/m³ and acceleration due to gravity is 10 m/s². The self-weight of the cylinder is negligible. The formula for hoop stress in a thin-walled cylinder can be used at all points along the height of the cylindrical container. The axial and circumferential stress \((\sigma_z, \sigma_c)\) experienced by the cylinder wall at mid-depth (1 m as shown) is

1. (10, 10) MPa
2. (5, 10) MPa
3. (10, 5) MPa
4. (5, 5) MPa

Correct answer: (5, 10) MPa

Solution

At 1 m below the free surface, pressure is \(p = \rho g h = 1000\times 10\times 1 = 10^4\,\text{Pa} = 0.01\,\text{MPa}\). For a thin cylinder, hoop stress is \(\sigma_c = pR/t = 0.01\times 1/0.001 = 10\,\text{MPa}\), and axial stress is half of that, \(\sigma_z = 5\,\text{MPa}\). Hence the stress pair is \((5,10)\,\text{MPa}\).

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