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A thick cylinder is subjected to an internal pressure of 60 MPa. If the hoop stress on the outer surface is 150 MPa, then the hoop stress on the internal surface is:
- a)105 MPa
- b)180 MPa
- c)210 MPa
- d)135 MPa
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A thick cylinder is subjected to an internal pressure of 60 MPa. If th...
If internal pressure = pi; External pressure = zero
Circumferential or hoop stress 
Most Upvoted Answer
A thick cylinder is subjected to an internal pressure of 60 MPa. If th...
**Explanation:**
To determine the hoop stress on the internal surface of the thick cylinder, we can use the formula for hoop stress:
**Hoop stress** (σ_h) = (p * r_i) / (r_o - r_i)
where:
- σ_h is the hoop stress
- p is the internal pressure
- r_i is the internal radius of the cylinder
- r_o is the external radius of the cylinder
Given data:
- Internal pressure (p) = 60 MPa
- Hoop stress on the outer surface (σ_o) = 150 MPa
We need to find the hoop stress on the internal surface (σ_i).
## Step 1: Finding the external radius (r_o)
The external radius (r_o) can be calculated using the hoop stress on the outer surface:
σ_o = (p * r_o) / (r_o - r_i)
Rearranging the equation:
(r_o - r_i) = (p * r_o) / σ_o
Substituting the given values:
(150 MPa) = (60 MPa * r_o) / (r_o - r_i)
Simplifying:
150 (r_o - r_i) = 60 r_o
150 r_o - 150 r_i = 60 r_o
90 r_o = 150 r_i
r_o = (150/90) r_i
r_o = (5/3) r_i
## Step 2: Finding the hoop stress on the internal surface (σ_i)
Now we can substitute the value of r_o in the equation for hoop stress:
σ_i = (p * r_i) / (r_o - r_i)
Substituting the known values:
σ_i = (60 MPa * r_i) / ((5/3) r_i - r_i)
Simplifying:
σ_i = (60 MPa * r_i) / ((5/3 - 1) r_i)
σ_i = (60 MPa * r_i) / (2/3 r_i)
σ_i = (90 MPa * r_i) / r_i
σ_i = 90 MPa
Therefore, the hoop stress on the internal surface is 90 MPa, which is not among the given options. However, it is important to note that 90 MPa is the correct answer based on the calculations. If none of the given options match the calculated value, there might be an error in the question or answer choices.
To determine the hoop stress on the internal surface of the thick cylinder, we can use the formula for hoop stress:
**Hoop stress** (σ_h) = (p * r_i) / (r_o - r_i)
where:
- σ_h is the hoop stress
- p is the internal pressure
- r_i is the internal radius of the cylinder
- r_o is the external radius of the cylinder
Given data:
- Internal pressure (p) = 60 MPa
- Hoop stress on the outer surface (σ_o) = 150 MPa
We need to find the hoop stress on the internal surface (σ_i).
## Step 1: Finding the external radius (r_o)
The external radius (r_o) can be calculated using the hoop stress on the outer surface:
σ_o = (p * r_o) / (r_o - r_i)
Rearranging the equation:
(r_o - r_i) = (p * r_o) / σ_o
Substituting the given values:
(150 MPa) = (60 MPa * r_o) / (r_o - r_i)
Simplifying:
150 (r_o - r_i) = 60 r_o
150 r_o - 150 r_i = 60 r_o
90 r_o = 150 r_i
r_o = (150/90) r_i
r_o = (5/3) r_i
## Step 2: Finding the hoop stress on the internal surface (σ_i)
Now we can substitute the value of r_o in the equation for hoop stress:
σ_i = (p * r_i) / (r_o - r_i)
Substituting the known values:
σ_i = (60 MPa * r_i) / ((5/3) r_i - r_i)
Simplifying:
σ_i = (60 MPa * r_i) / ((5/3 - 1) r_i)
σ_i = (60 MPa * r_i) / (2/3 r_i)
σ_i = (90 MPa * r_i) / r_i
σ_i = 90 MPa
Therefore, the hoop stress on the internal surface is 90 MPa, which is not among the given options. However, it is important to note that 90 MPa is the correct answer based on the calculations. If none of the given options match the calculated value, there might be an error in the question or answer choices.
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A thick cylinder is subjected to an internal pressure of 60 MPa. If the hoop stress on the outer surface is 150 MPa, then the hoop stress on the internal surface is:a)105 MPab)180 MPac)210 MPad)135 MPaCorrect answer is option 'C'. Can you explain this answer?
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A thick cylinder is subjected to an internal pressure of 60 MPa. If the hoop stress on the outer surface is 150 MPa, then the hoop stress on the internal surface is:a)105 MPab)180 MPac)210 MPad)135 MPaCorrect answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A thick cylinder is subjected to an internal pressure of 60 MPa. If the hoop stress on the outer surface is 150 MPa, then the hoop stress on the internal surface is:a)105 MPab)180 MPac)210 MPad)135 MPaCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A thick cylinder is subjected to an internal pressure of 60 MPa. If the hoop stress on the outer surface is 150 MPa, then the hoop stress on the internal surface is:a)105 MPab)180 MPac)210 MPad)135 MPaCorrect answer is option 'C'. Can you explain this answer?.
A thick cylinder is subjected to an internal pressure of 60 MPa. If the hoop stress on the outer surface is 150 MPa, then the hoop stress on the internal surface is:a)105 MPab)180 MPac)210 MPad)135 MPaCorrect answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A thick cylinder is subjected to an internal pressure of 60 MPa. If the hoop stress on the outer surface is 150 MPa, then the hoop stress on the internal surface is:a)105 MPab)180 MPac)210 MPad)135 MPaCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A thick cylinder is subjected to an internal pressure of 60 MPa. If the hoop stress on the outer surface is 150 MPa, then the hoop stress on the internal surface is:a)105 MPab)180 MPac)210 MPad)135 MPaCorrect answer is option 'C'. Can you explain this answer?.
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