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A steel rod of 3 cm diameter and 5 m length is rigidly fixed at the left end and the right end is at a gap of 5 mm from the support. The rod is maintained at a temperature of 30°C. If the temperature is raised to 95°C, then the axial stress in the rod (in MPa) is ___________.
Take E = 200 GPa and a = 12 x 10-6/°C
Correct answer is '0'. Can you explain this answer?
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Most Upvoted Answer
A steel rod of 3 cm diameter and 5 m length is rigidly fixed at the l...
Given:
Diameter of the steel rod = 3 cm = 0.03 m
Length of the steel rod = 5 m
Gap between the right end and the support = 5 mm = 0.005 m
Initial temperature of the rod (T1) = 30°C
Final temperature of the rod (T2) = 95°C
Young's modulus of steel (E) = 200 GPa = 200 × 10^9 Pa
Coefficient of linear expansion of steel (α) = 12 × 10^(-6)/°C
Solution:
Step 1: Calculate the change in length of the rod:
The change in length of a material can be calculated using the formula:
ΔL = α × L × ΔT
where ΔL is the change in length, α is the coefficient of linear expansion, L is the initial length, and ΔT is the change in temperature.
Given:
α = 12 × 10^(-6)/°C
L = 5 m
ΔT = T2 - T1 = 95°C - 30°C = 65°C
Substituting the values, we get:
ΔL = (12 × 10^(-6)/°C) × (5 m) × (65°C)
ΔL = 3.9 × 10^(-3) m
Step 2: Calculate the change in diameter of the rod:
The change in diameter of a material can be calculated using the formula:
ΔD = 2α × D × ΔT
where ΔD is the change in diameter, α is the coefficient of linear expansion, D is the initial diameter, and ΔT is the change in temperature.
Given:
α = 12 × 10^(-6)/°C
D = 3 cm = 0.03 m
ΔT = 65°C
Substituting the values, we get:
ΔD = (2 × 12 × 10^(-6)/°C) × (0.03 m) × (65°C)
ΔD = 4.68 × 10^(-6) m
Step 3: Calculate the change in cross-sectional area of the rod:
The change in cross-sectional area of a rod can be calculated using the formula:
ΔA = π/4 × (D^2 - (D - ΔD)^2)
where ΔA is the change in cross-sectional area, D is the initial diameter, and ΔD is the change in diameter.
Given:
D = 0.03 m
ΔD = 4.68 × 10^(-6) m
Substituting the values, we get:
ΔA = π/4 × (0.03^2 - (0.03 - 4.68 × 10^(-6))^2)
ΔA = 1.77 × 10^(-8) m^2
Step 4: Calculate the change in volume of the rod:
The change in volume of a rod can be calculated using the formula:
ΔV = ΔA × L
where ΔV is the change in volume, ΔA is the change in cross-sectional area, and
Diameter of the steel rod = 3 cm = 0.03 m
Length of the steel rod = 5 m
Gap between the right end and the support = 5 mm = 0.005 m
Initial temperature of the rod (T1) = 30°C
Final temperature of the rod (T2) = 95°C
Young's modulus of steel (E) = 200 GPa = 200 × 10^9 Pa
Coefficient of linear expansion of steel (α) = 12 × 10^(-6)/°C
Solution:
Step 1: Calculate the change in length of the rod:
The change in length of a material can be calculated using the formula:
ΔL = α × L × ΔT
where ΔL is the change in length, α is the coefficient of linear expansion, L is the initial length, and ΔT is the change in temperature.
Given:
α = 12 × 10^(-6)/°C
L = 5 m
ΔT = T2 - T1 = 95°C - 30°C = 65°C
Substituting the values, we get:
ΔL = (12 × 10^(-6)/°C) × (5 m) × (65°C)
ΔL = 3.9 × 10^(-3) m
Step 2: Calculate the change in diameter of the rod:
The change in diameter of a material can be calculated using the formula:
ΔD = 2α × D × ΔT
where ΔD is the change in diameter, α is the coefficient of linear expansion, D is the initial diameter, and ΔT is the change in temperature.
Given:
α = 12 × 10^(-6)/°C
D = 3 cm = 0.03 m
ΔT = 65°C
Substituting the values, we get:
ΔD = (2 × 12 × 10^(-6)/°C) × (0.03 m) × (65°C)
ΔD = 4.68 × 10^(-6) m
Step 3: Calculate the change in cross-sectional area of the rod:
The change in cross-sectional area of a rod can be calculated using the formula:
ΔA = π/4 × (D^2 - (D - ΔD)^2)
where ΔA is the change in cross-sectional area, D is the initial diameter, and ΔD is the change in diameter.
Given:
D = 0.03 m
ΔD = 4.68 × 10^(-6) m
Substituting the values, we get:
ΔA = π/4 × (0.03^2 - (0.03 - 4.68 × 10^(-6))^2)
ΔA = 1.77 × 10^(-8) m^2
Step 4: Calculate the change in volume of the rod:
The change in volume of a rod can be calculated using the formula:
ΔV = ΔA × L
where ΔV is the change in volume, ΔA is the change in cross-sectional area, and
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Community Answer
A steel rod of 3 cm diameter and 5 m length is rigidly fixed at the l...
Change in length of the rod due to change in temperature,
(Δl)thermal = lαΔt
= 5000 x 12 x 10-6 x 65 = 3.9 mm
∴ Elongation = 3.9 mm
Given gap = 5 mm
Thus, elongation < gap="" ⇒="" free="" />
∴ No axial stress is developed
σth = 0 MPa
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A steel rod of 3 cm diameter and 5 m length is rigidly fixed at the left end and the right end is at a gap of 5 mm from the support. The rod is maintained at a temperature of 30°C. If the temperature is raised to 95°C, then the axial stress in the rod (in MPa) is ___________.Take E = 200 GPa and a = 12 x 10-6/°CCorrect answer is '0'. Can you explain this answer?
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A steel rod of 3 cm diameter and 5 m length is rigidly fixed at the left end and the right end is at a gap of 5 mm from the support. The rod is maintained at a temperature of 30°C. If the temperature is raised to 95°C, then the axial stress in the rod (in MPa) is ___________.Take E = 200 GPa and a = 12 x 10-6/°CCorrect answer is '0'. 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 steel rod of 3 cm diameter and 5 m length is rigidly fixed at the left end and the right end is at a gap of 5 mm from the support. The rod is maintained at a temperature of 30°C. If the temperature is raised to 95°C, then the axial stress in the rod (in MPa) is ___________.Take E = 200 GPa and a = 12 x 10-6/°CCorrect answer is '0'. 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 steel rod of 3 cm diameter and 5 m length is rigidly fixed at the left end and the right end is at a gap of 5 mm from the support. The rod is maintained at a temperature of 30°C. If the temperature is raised to 95°C, then the axial stress in the rod (in MPa) is ___________.Take E = 200 GPa and a = 12 x 10-6/°CCorrect answer is '0'. Can you explain this answer?.
A steel rod of 3 cm diameter and 5 m length is rigidly fixed at the left end and the right end is at a gap of 5 mm from the support. The rod is maintained at a temperature of 30°C. If the temperature is raised to 95°C, then the axial stress in the rod (in MPa) is ___________.Take E = 200 GPa and a = 12 x 10-6/°CCorrect answer is '0'. 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 steel rod of 3 cm diameter and 5 m length is rigidly fixed at the left end and the right end is at a gap of 5 mm from the support. The rod is maintained at a temperature of 30°C. If the temperature is raised to 95°C, then the axial stress in the rod (in MPa) is ___________.Take E = 200 GPa and a = 12 x 10-6/°CCorrect answer is '0'. 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 steel rod of 3 cm diameter and 5 m length is rigidly fixed at the left end and the right end is at a gap of 5 mm from the support. The rod is maintained at a temperature of 30°C. If the temperature is raised to 95°C, then the axial stress in the rod (in MPa) is ___________.Take E = 200 GPa and a = 12 x 10-6/°CCorrect answer is '0'. Can you explain this answer?.
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A steel rod of 3 cm diameter and 5 m length is rigidly fixed at the left end and the right end is at a gap of 5 mm from the support. The rod is maintained at a temperature of 30°C. If the temperature is raised to 95°C, then the axial stress in the rod (in MPa) is ___________.Take E = 200 GPa and a = 12 x 10-6/°CCorrect answer is '0'. Can you explain this answer?, a detailed solution for A steel rod of 3 cm diameter and 5 m length is rigidly fixed at the left end and the right end is at a gap of 5 mm from the support. The rod is maintained at a temperature of 30°C. If the temperature is raised to 95°C, then the axial stress in the rod (in MPa) is ___________.Take E = 200 GPa and a = 12 x 10-6/°CCorrect answer is '0'. Can you explain this answer? has been provided alongside types of A steel rod of 3 cm diameter and 5 m length is rigidly fixed at the left end and the right end is at a gap of 5 mm from the support. The rod is maintained at a temperature of 30°C. If the temperature is raised to 95°C, then the axial stress in the rod (in MPa) is ___________.Take E = 200 GPa and a = 12 x 10-6/°CCorrect answer is '0'. Can you explain this answer? theory, EduRev gives you an
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