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A rod tapers uniformly from 30 mm to 15 mm diameter in a length of 300 mm. If the rod is to be subjected to an axial load of 600 N, then the extension of the rod is (Answer up to four decimal places)
(Take E = 2 105 N/mm2)
Correct answer is '0.0025'. Can you explain this answer?
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A rod tapers uniformly from 30 mm to 15 mm diameter in a length of 30...
Extension of a Tapered Rod under Axial Load
Given:
- Diameter at one end of the rod (D1) = 30 mm
- Diameter at the other end of the rod (D2) = 15 mm
- Length of the rod (L) = 300 mm
- Axial load applied to the rod (P) = 600 N
- Young's modulus of the material (E) = 2 x 10^5 N/mm^2
To find:
- Extension of the rod (ΔL)
Formula:
The extension of a rod under axial load can be calculated using Hooke's Law, which states that the elongation of a material is directly proportional to the applied load and the material's modulus of elasticity:
ΔL = (P * L) / (A * E)
Where:
ΔL = Extension of the rod
P = Axial load applied to the rod
L = Length of the rod
A = Area of the rod
E = Young's modulus of the material
Area of the Tapered Rod:
The area of a rod with varying diameter can be calculated using the formula for the area of a circle:
A = π * d^2 / 4
Where:
A = Area of the rod
π = 3.14159 (approximately)
d = Diameter of the rod at a specific point
Calculation:
1. Calculate the area of the rod at the larger end:
A1 = π * (D1^2) / 4
2. Calculate the area of the rod at the smaller end:
A2 = π * (D2^2) / 4
3. Calculate the average area of the rod:
A_avg = (A1 + A2) / 2
4. Calculate the extension of the rod:
ΔL = (P * L) / (A_avg * E)
Substituting the given values into the formula:
A1 = π * (30^2) / 4 = 706.8583 mm^2
A2 = π * (15^2) / 4 = 176.7146 mm^2
A_avg = (706.8583 + 176.7146) / 2 = 441.7864 mm^2
ΔL = (600 * 300) / (441.7864 * 2 x 10^5) = 0.0025 mm (rounded to four decimal places)
Hence, the extension of the rod under the given axial load is 0.0025 mm.
Given:
- Diameter at one end of the rod (D1) = 30 mm
- Diameter at the other end of the rod (D2) = 15 mm
- Length of the rod (L) = 300 mm
- Axial load applied to the rod (P) = 600 N
- Young's modulus of the material (E) = 2 x 10^5 N/mm^2
To find:
- Extension of the rod (ΔL)
Formula:
The extension of a rod under axial load can be calculated using Hooke's Law, which states that the elongation of a material is directly proportional to the applied load and the material's modulus of elasticity:
ΔL = (P * L) / (A * E)
Where:
ΔL = Extension of the rod
P = Axial load applied to the rod
L = Length of the rod
A = Area of the rod
E = Young's modulus of the material
Area of the Tapered Rod:
The area of a rod with varying diameter can be calculated using the formula for the area of a circle:
A = π * d^2 / 4
Where:
A = Area of the rod
π = 3.14159 (approximately)
d = Diameter of the rod at a specific point
Calculation:
1. Calculate the area of the rod at the larger end:
A1 = π * (D1^2) / 4
2. Calculate the area of the rod at the smaller end:
A2 = π * (D2^2) / 4
3. Calculate the average area of the rod:
A_avg = (A1 + A2) / 2
4. Calculate the extension of the rod:
ΔL = (P * L) / (A_avg * E)
Substituting the given values into the formula:
A1 = π * (30^2) / 4 = 706.8583 mm^2
A2 = π * (15^2) / 4 = 176.7146 mm^2
A_avg = (706.8583 + 176.7146) / 2 = 441.7864 mm^2
ΔL = (600 * 300) / (441.7864 * 2 x 10^5) = 0.0025 mm (rounded to four decimal places)
Hence, the extension of the rod under the given axial load is 0.0025 mm.
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A rod tapers uniformly from 30 mm to 15 mm diameter in a length of 300 mm. If the rod is to be subjected to an axial load of 600 N, then the extension of the rod is (Answer up to four decimal places)(Take E = 2 105 N/mm2)Correct answer is '0.0025'. Can you explain this answer?
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A rod tapers uniformly from 30 mm to 15 mm diameter in a length of 300 mm. If the rod is to be subjected to an axial load of 600 N, then the extension of the rod is (Answer up to four decimal places)(Take E = 2 105 N/mm2)Correct answer is '0.0025'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A rod tapers uniformly from 30 mm to 15 mm diameter in a length of 300 mm. If the rod is to be subjected to an axial load of 600 N, then the extension of the rod is (Answer up to four decimal places)(Take E = 2 105 N/mm2)Correct answer is '0.0025'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rod tapers uniformly from 30 mm to 15 mm diameter in a length of 300 mm. If the rod is to be subjected to an axial load of 600 N, then the extension of the rod is (Answer up to four decimal places)(Take E = 2 105 N/mm2)Correct answer is '0.0025'. Can you explain this answer?.
A rod tapers uniformly from 30 mm to 15 mm diameter in a length of 300 mm. If the rod is to be subjected to an axial load of 600 N, then the extension of the rod is (Answer up to four decimal places)(Take E = 2 105 N/mm2)Correct answer is '0.0025'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about A rod tapers uniformly from 30 mm to 15 mm diameter in a length of 300 mm. If the rod is to be subjected to an axial load of 600 N, then the extension of the rod is (Answer up to four decimal places)(Take E = 2 105 N/mm2)Correct answer is '0.0025'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rod tapers uniformly from 30 mm to 15 mm diameter in a length of 300 mm. If the rod is to be subjected to an axial load of 600 N, then the extension of the rod is (Answer up to four decimal places)(Take E = 2 105 N/mm2)Correct answer is '0.0025'. Can you explain this answer?.
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A rod tapers uniformly from 30 mm to 15 mm diameter in a length of 300 mm. If the rod is to be subjected to an axial load of 600 N, then the extension of the rod is (Answer up to four decimal places)(Take E = 2 105 N/mm2)Correct answer is '0.0025'. Can you explain this answer?, a detailed solution for A rod tapers uniformly from 30 mm to 15 mm diameter in a length of 300 mm. If the rod is to be subjected to an axial load of 600 N, then the extension of the rod is (Answer up to four decimal places)(Take E = 2 105 N/mm2)Correct answer is '0.0025'. Can you explain this answer? has been provided alongside types of A rod tapers uniformly from 30 mm to 15 mm diameter in a length of 300 mm. If the rod is to be subjected to an axial load of 600 N, then the extension of the rod is (Answer up to four decimal places)(Take E = 2 105 N/mm2)Correct answer is '0.0025'. Can you explain this answer? theory, EduRev gives you an
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