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A thick-walled hollow cylinder having outside and inside radii of 90 mm and 40 mm respectively is subjected to an external pressure of 800 MN/m2. The maximum circumferential stress in the cylinder will occur at a radius of 
  • a)
    40 mm
  • b)
    60 mm
  • c)
    65 mm
  • d)
    90 mm
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A thick-walled hollow cylinder having outside and inside radii of 90 m...
**Given:**
- Outside radius of the cylinder (r1) = 90 mm
- Inside radius of the cylinder (r2) = 40 mm
- External pressure (P) = 800 MN/m2

**To find:**
- The maximum circumferential stress in the cylinder will occur at which radius?

**Assumption:**
- The cylinder is assumed to be thin-walled, which means the thickness of the wall is negligible compared to the radius.
- The cylinder is assumed to be homogeneous and isotropic, with uniform properties throughout.

**Formula used:**
- The circumferential stress (σc) in a thin-walled cylinder is given by the formula: σc = P * r / t
- Where P is the external pressure
- r is the radius at which the stress is to be determined
- t is the thickness of the cylinder wall

**Explanation:**
To find the maximum circumferential stress in the cylinder, we need to determine the radius at which the stress is the highest. This occurs at the inner surface of the cylinder, where the radius is equal to the inside radius (r2).

Using the formula for circumferential stress, we can calculate the stress at the inner surface of the cylinder:
σc = P * r2 / t

Since the thickness of the wall (t) is not given, we can assume it to be the difference between the outside radius and the inside radius of the cylinder:
t = r1 - r2

Substituting the values into the formula, we get:
σc = P * r2 / (r1 - r2)

Plugging in the given values:
σc = 800 MN/m2 * 40 mm / (90 mm - 40 mm)
σc = 800 MN/m2 * 40 mm / 50 mm
σc = 640 MN/m2

Therefore, the maximum circumferential stress in the cylinder occurs at a radius of 40 mm (option A).
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Community Answer
A thick-walled hollow cylinder having outside and inside radii of 90 m...
40
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A thick-walled hollow cylinder having outside and inside radii of 90 mm and 40 mm respectively is subjected to an external pressure of 800 MN/m2. The maximum circumferential stress in the cylinder will occur at a radius ofa)40 mmb)60 mmc)65 mmd)90 mmCorrect answer is option 'A'. Can you explain this answer?
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