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A spherical vessel with an inside diameter of 2 m is made of material having an allowable stress in tension of 500 kg/cm2. The thickness of a shell to with stand a pressure of 25 kg/cm2 should be:
- a)5 cm
- b)10 cm
- c)2.5 cm
- d)1.25 cm
Correct answer is option 'C'. Can you explain this answer?
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To determine the thickness of the shell required to withstand a given pressure, we can use the formulas for the stress and strain in a thin-walled spherical vessel.
The formula for the stress in a thin-walled spherical vessel is given by:
σ = P * r / t
where σ is the stress, P is the pressure, r is the radius of the vessel, and t is the thickness of the shell.
The formula for the strain in a thin-walled spherical vessel is given by:
ε = Δr / r
where ε is the strain and Δr is the change in radius.
Since the vessel is spherical, the change in radius is equal to the thickness of the shell, i.e., Δr = t.
From the given information, the inside diameter of the vessel is 2 m, so the radius is 1 m. The pressure that the shell needs to withstand is 25 kg/cm2.
Now we can substitute these values into the stress formula to find the required thickness of the shell:
500 kg/cm2 = 25 kg/cm2 * 1 m / t
Simplifying this equation, we get:
t = (25 kg/cm2 * 1 m) / 500 kg/cm2
t = 0.05 m
Since the thickness is given in meters, we need to convert it to centimeters:
t = 0.05 m * 100 cm/m
t = 5 cm
Thus, the correct answer is option C) 2.5 cm.
The formula for the stress in a thin-walled spherical vessel is given by:
σ = P * r / t
where σ is the stress, P is the pressure, r is the radius of the vessel, and t is the thickness of the shell.
The formula for the strain in a thin-walled spherical vessel is given by:
ε = Δr / r
where ε is the strain and Δr is the change in radius.
Since the vessel is spherical, the change in radius is equal to the thickness of the shell, i.e., Δr = t.
From the given information, the inside diameter of the vessel is 2 m, so the radius is 1 m. The pressure that the shell needs to withstand is 25 kg/cm2.
Now we can substitute these values into the stress formula to find the required thickness of the shell:
500 kg/cm2 = 25 kg/cm2 * 1 m / t
Simplifying this equation, we get:
t = (25 kg/cm2 * 1 m) / 500 kg/cm2
t = 0.05 m
Since the thickness is given in meters, we need to convert it to centimeters:
t = 0.05 m * 100 cm/m
t = 5 cm
Thus, the correct answer is option C) 2.5 cm.
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A spherical vessel with an inside diameter of 2 m is made of material having an allowable stress in tension of 500 kg/cm2. The thickness of a shell to with stand a pressure of 25 kg/cm2should be:a)5 cmb)10 cmc)2.5 cmd)1.25 cmCorrect answer is option 'C'. Can you explain this answer?
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A spherical vessel with an inside diameter of 2 m is made of material having an allowable stress in tension of 500 kg/cm2. The thickness of a shell to with stand a pressure of 25 kg/cm2should be:a)5 cmb)10 cmc)2.5 cmd)1.25 cmCorrect answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A spherical vessel with an inside diameter of 2 m is made of material having an allowable stress in tension of 500 kg/cm2. The thickness of a shell to with stand a pressure of 25 kg/cm2should be:a)5 cmb)10 cmc)2.5 cmd)1.25 cmCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A spherical vessel with an inside diameter of 2 m is made of material having an allowable stress in tension of 500 kg/cm2. The thickness of a shell to with stand a pressure of 25 kg/cm2should be:a)5 cmb)10 cmc)2.5 cmd)1.25 cmCorrect answer is option 'C'. Can you explain this answer?.
A spherical vessel with an inside diameter of 2 m is made of material having an allowable stress in tension of 500 kg/cm2. The thickness of a shell to with stand a pressure of 25 kg/cm2should be:a)5 cmb)10 cmc)2.5 cmd)1.25 cmCorrect answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about A spherical vessel with an inside diameter of 2 m is made of material having an allowable stress in tension of 500 kg/cm2. The thickness of a shell to with stand a pressure of 25 kg/cm2should be:a)5 cmb)10 cmc)2.5 cmd)1.25 cmCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A spherical vessel with an inside diameter of 2 m is made of material having an allowable stress in tension of 500 kg/cm2. The thickness of a shell to with stand a pressure of 25 kg/cm2should be:a)5 cmb)10 cmc)2.5 cmd)1.25 cmCorrect answer is option 'C'. Can you explain this answer?.
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