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A conical bar having density of 25 g/cm3 elongates due to its own weight. If the length of the bar is 6 m and the largest diameter of the bar is 2 m, then the total elongation is ____________ μ m. (Assume E = 80 Gpa, g = 9.81 m/s2) (Answer up to two decimal places)
Correct answer is '18.39'. Can you explain this answer?
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A conical bar having density of 25 g/cm3 elongates due to its own wei...
= 18.39375 μm
= 18.39 μm
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A conical bar having density of 25 g/cm3 elongates due to its own wei...
Given:
Density of the bar (ρ) = 25 g/cm³
Length of the bar (L) = 6 m
Largest diameter of the bar (D) = 2 m
Young's modulus of elasticity (E) = 80 GPa = 80 × 10⁹ Pa
Acceleration due to gravity (g) = 9.81 m/s²
To find:
Total elongation of the bar in μm
Solution:
Step 1: Finding the volume of the bar:
The volume of a cone can be calculated using the formula:
V = (1/3) × π × r² × h
Where V is the volume, π is a constant (approximately 3.14), r is the radius of the base, and h is the height.
Given that the largest diameter of the bar is 2 m, the radius (r) is half of that:
r = D/2 = 2/2 = 1 m
The height (h) of the cone is equal to the length of the bar (L) since the bar is in the shape of a cone:
h = L = 6 m
Substituting the values into the volume formula:
V = (1/3) × π × (1 m)² × (6 m)
V = (1/3) × 3.14 × 1 m² × 6 m
V = 6.28 m³
Step 2: Finding the mass of the bar:
The mass of an object can be calculated using the formula:
m = ρ × V
Where m is the mass, ρ is the density, and V is the volume.
Substituting the values:
m = (25 g/cm³) × (6.28 m³)
Convert g/cm³ to kg/m³ by multiplying by 1000:
m = (25 × 1000 kg/m³) × (6.28 m³)
m = 157000 kg
Step 3: Finding the weight of the bar:
The weight of an object can be calculated using the formula:
W = m × g
Where W is the weight, m is the mass, and g is the acceleration due to gravity.
Substituting the values:
W = (157000 kg) × (9.81 m/s²)
W = 1538610 N
Step 4: Finding the stress in the bar:
Stress can be calculated using the formula:
Stress = Weight / Area
Where Stress is the stress, Weight is the weight, and Area is the cross-sectional area of the bar.
The cross-sectional area of a cone can be calculated using the formula:
Area = (π / 4) × (D² - d²)
Where D is the largest diameter and d is the smallest diameter.
Given that the largest diameter is 2 m and the smallest diameter is 0 (since it elongates due to its own weight):
Area = (3.14 / 4) × (2 m)²
Area = 3.14 m²
Substituting the values into the stress formula:
Stress = (1538610 N) / (3.14 m²)
Stress = 489682.165
Density of the bar (ρ) = 25 g/cm³
Length of the bar (L) = 6 m
Largest diameter of the bar (D) = 2 m
Young's modulus of elasticity (E) = 80 GPa = 80 × 10⁹ Pa
Acceleration due to gravity (g) = 9.81 m/s²
To find:
Total elongation of the bar in μm
Solution:
Step 1: Finding the volume of the bar:
The volume of a cone can be calculated using the formula:
V = (1/3) × π × r² × h
Where V is the volume, π is a constant (approximately 3.14), r is the radius of the base, and h is the height.
Given that the largest diameter of the bar is 2 m, the radius (r) is half of that:
r = D/2 = 2/2 = 1 m
The height (h) of the cone is equal to the length of the bar (L) since the bar is in the shape of a cone:
h = L = 6 m
Substituting the values into the volume formula:
V = (1/3) × π × (1 m)² × (6 m)
V = (1/3) × 3.14 × 1 m² × 6 m
V = 6.28 m³
Step 2: Finding the mass of the bar:
The mass of an object can be calculated using the formula:
m = ρ × V
Where m is the mass, ρ is the density, and V is the volume.
Substituting the values:
m = (25 g/cm³) × (6.28 m³)
Convert g/cm³ to kg/m³ by multiplying by 1000:
m = (25 × 1000 kg/m³) × (6.28 m³)
m = 157000 kg
Step 3: Finding the weight of the bar:
The weight of an object can be calculated using the formula:
W = m × g
Where W is the weight, m is the mass, and g is the acceleration due to gravity.
Substituting the values:
W = (157000 kg) × (9.81 m/s²)
W = 1538610 N
Step 4: Finding the stress in the bar:
Stress can be calculated using the formula:
Stress = Weight / Area
Where Stress is the stress, Weight is the weight, and Area is the cross-sectional area of the bar.
The cross-sectional area of a cone can be calculated using the formula:
Area = (π / 4) × (D² - d²)
Where D is the largest diameter and d is the smallest diameter.
Given that the largest diameter is 2 m and the smallest diameter is 0 (since it elongates due to its own weight):
Area = (3.14 / 4) × (2 m)²
Area = 3.14 m²
Substituting the values into the stress formula:
Stress = (1538610 N) / (3.14 m²)
Stress = 489682.165
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A conical bar having density of 25 g/cm3 elongates due to its own weight. If the length of the bar is 6 m and the largest diameter of the bar is 2 m, then the total elongation is ____________ μ m. (Assume E = 80 Gpa, g = 9.81 m/s2) (Answer up to two decimal places)Correct answer is '18.39'. Can you explain this answer?
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A conical bar having density of 25 g/cm3 elongates due to its own weight. If the length of the bar is 6 m and the largest diameter of the bar is 2 m, then the total elongation is ____________ μ m. (Assume E = 80 Gpa, g = 9.81 m/s2) (Answer up to two decimal places)Correct answer is '18.39'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about A conical bar having density of 25 g/cm3 elongates due to its own weight. If the length of the bar is 6 m and the largest diameter of the bar is 2 m, then the total elongation is ____________ μ m. (Assume E = 80 Gpa, g = 9.81 m/s2) (Answer up to two decimal places)Correct answer is '18.39'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A conical bar having density of 25 g/cm3 elongates due to its own weight. If the length of the bar is 6 m and the largest diameter of the bar is 2 m, then the total elongation is ____________ μ m. (Assume E = 80 Gpa, g = 9.81 m/s2) (Answer up to two decimal places)Correct answer is '18.39'. Can you explain this answer?.
A conical bar having density of 25 g/cm3 elongates due to its own weight. If the length of the bar is 6 m and the largest diameter of the bar is 2 m, then the total elongation is ____________ μ m. (Assume E = 80 Gpa, g = 9.81 m/s2) (Answer up to two decimal places)Correct answer is '18.39'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about A conical bar having density of 25 g/cm3 elongates due to its own weight. If the length of the bar is 6 m and the largest diameter of the bar is 2 m, then the total elongation is ____________ μ m. (Assume E = 80 Gpa, g = 9.81 m/s2) (Answer up to two decimal places)Correct answer is '18.39'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A conical bar having density of 25 g/cm3 elongates due to its own weight. If the length of the bar is 6 m and the largest diameter of the bar is 2 m, then the total elongation is ____________ μ m. (Assume E = 80 Gpa, g = 9.81 m/s2) (Answer up to two decimal places)Correct answer is '18.39'. Can you explain this answer?.
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A conical bar having density of 25 g/cm3 elongates due to its own weight. If the length of the bar is 6 m and the largest diameter of the bar is 2 m, then the total elongation is ____________ μ m. (Assume E = 80 Gpa, g = 9.81 m/s2) (Answer up to two decimal places)Correct answer is '18.39'. Can you explain this answer?, a detailed solution for A conical bar having density of 25 g/cm3 elongates due to its own weight. If the length of the bar is 6 m and the largest diameter of the bar is 2 m, then the total elongation is ____________ μ m. (Assume E = 80 Gpa, g = 9.81 m/s2) (Answer up to two decimal places)Correct answer is '18.39'. Can you explain this answer? has been provided alongside types of A conical bar having density of 25 g/cm3 elongates due to its own weight. If the length of the bar is 6 m and the largest diameter of the bar is 2 m, then the total elongation is ____________ μ m. (Assume E = 80 Gpa, g = 9.81 m/s2) (Answer up to two decimal places)Correct answer is '18.39'. Can you explain this answer? theory, EduRev gives you an
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