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The piston rod of diameter 20 mm and length 700 mm in a hydraulic cylinder is subjected to a compressive force of 10 KN due to the internal pressure. The end conditions for the rod may be assumed as guided at the piston end and hinged at the other end. The Young’s modulus is 200 GPa. The factor of safety for the piston rod is
  • a)
    0.68
  • b)
    2.75
  • c)
    5.62
  • d)
    11.0
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The piston rod of diameter 20 mm and length 700 mm in a hydraulic cyli...
Given : Diameter (d) = 20 mm

Length (L) = 700 mm

Force (P) = 10 kN (compressive)

Assuming guided end to be fixed and other end given as hinged. The crippling load according to Euler’s equation.
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Most Upvoted Answer
The piston rod of diameter 20 mm and length 700 mm in a hydraulic cyli...
's modulus of the material of the rod is 200 GPa.

To determine the stress in the piston rod, we can use the formula for axial stress:

Stress = Force / Area

The area of the piston rod can be calculated using the formula for the area of a circle:

Area = π * (diameter/2)^2

Plugging in the given values, we can calculate the area:

Area = π * (20 mm / 2)^2
Area = π * (10 mm)^2
Area = 100π mm^2

Converting the area from mm^2 to m^2:

Area = 100π * (1 m / 1000 mm)^2
Area = 100π * (1/1000)^2 m^2
Area = π/1000 m^2

Plugging in the given force and calculated area, we can calculate the stress:

Stress = 10 kN / (π/1000 m^2)
Stress = 10 * 1000 N / π m^2
Stress = 10000/π N/m^2

The Young's modulus of the material is given as 200 GPa, which is equivalent to 200 * 10^9 N/m^2.

The strain in the rod can be calculated using Hooke's Law:

Strain = Stress / Young's modulus

Plugging in the calculated stress and given Young's modulus, we can calculate the strain:

Strain = (10000/π N/m^2) / (200 * 10^9 N/m^2)
Strain = (10000/π) / (200 * 10^9) 1/m
Strain = 5 / (π * 10^12) 1/m

Therefore, the stress in the piston rod is 10000/π N/m^2 and the strain in the rod is 5 / (π * 10^12) 1/m.
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Community Answer
The piston rod of diameter 20 mm and length 700 mm in a hydraulic cyli...
B
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The piston rod of diameter 20 mm and length 700 mm in a hydraulic cylinder is subjected to a compressive force of 10 KN due to the internal pressure. The end conditions for the rod may be assumed as guided at the piston end and hinged at the other end. The Young’s modulus is 200 GPa. The factor of safety for the piston rod isa)0.68b)2.75c)5.62d)11.0Correct answer is option 'C'. Can you explain this answer?
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The piston rod of diameter 20 mm and length 700 mm in a hydraulic cylinder is subjected to a compressive force of 10 KN due to the internal pressure. The end conditions for the rod may be assumed as guided at the piston end and hinged at the other end. The Young’s modulus is 200 GPa. The factor of safety for the piston rod isa)0.68b)2.75c)5.62d)11.0Correct 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 The piston rod of diameter 20 mm and length 700 mm in a hydraulic cylinder is subjected to a compressive force of 10 KN due to the internal pressure. The end conditions for the rod may be assumed as guided at the piston end and hinged at the other end. The Young’s modulus is 200 GPa. The factor of safety for the piston rod isa)0.68b)2.75c)5.62d)11.0Correct 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 The piston rod of diameter 20 mm and length 700 mm in a hydraulic cylinder is subjected to a compressive force of 10 KN due to the internal pressure. The end conditions for the rod may be assumed as guided at the piston end and hinged at the other end. The Young’s modulus is 200 GPa. The factor of safety for the piston rod isa)0.68b)2.75c)5.62d)11.0Correct answer is option 'C'. Can you explain this answer?.
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