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A thin walled spherical shell is subjected to an internal pressure. If the radius of the shell is increased by 1% and the thickness is reduced by 1%, with the internal pressure remaining the same, the percentage change in the circumferential (hoop) stress is
  • a)
    0
  • b)
    1
  • c)
    1.08
  • d)
    2.02
Correct answer is option 'D'. Can you explain this answer?
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A thin walled spherical shell is subjected to an internal pressure. If...
For thin walled spherical shell circumferential (hoop) stress is given by
Now, radius of the shell is increased by 1% and the thickness is reduced by 1%,with the internal pressure remaining the same,
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A thin walled spherical shell is subjected to an internal pressure. If...
Explanation:

Given:
- Increase in radius: 1%
- Decrease in thickness: 1%
- Internal pressure remains the same

Formula for Hoop Stress:
Hoop stress (σh) = (Pr) / t

Calculation:
- Let the original radius be R and the original thickness be t.
- The new radius is 1% more than R i.e. R' = 1.01R
- The new thickness is 1% less than t i.e. t' = 0.99t

Original Hoop Stress:
σh = (PR) / t

New Hoop Stress:
σh' = (P * 1.01R) / 0.99t

Percentage Change in Hoop Stress:
% Change = [(σh' - σh) / σh] * 100
Substitute the values and simplify to get:
% Change = 2.02%
Therefore, the percentage change in the circumferential (hoop) stress is 2.02%, which corresponds to option D.
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A thin walled spherical shell is subjected to an internal pressure. If...

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A thin walled spherical shell is subjected to an internal pressure. If the radius of the shell isincreased by 1% and the thickness is reduced by 1%, with the internal pressure remaining the same,the percentage change in the circumferential (hoop) stress isa)0b)1c)1.08d)2.02Correct answer is option 'D'. Can you explain this answer?
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