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A closely-coiled helical spring is made of 10 mm diameter steel wire, with the coil consisting of 10 turns with a mean diameter 120 mm. The spring carries an axial pull of 200 N. What is the value of shear stress induced in the spring neglecting the effect of stress concentration and of deflection in the spring, when the modulus of rigidity is 80 kN/mm2?
- a)61.1 N/mm2 and 34.6 N/mm2
- b)54.2 N/mm2 and 34.6 N/mm2
- c)63.5 N/mm2 and 42.6 N/mm2
- d)54.2 N/mm2 and 42.6 N/mm2
Correct answer is option 'A'. Can you explain this answer?
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A closely-coiled helical spring is made of 10 mm diameter steel wire,...
To calculate the value of shear stress induced in the spring, we can use the formula for shear stress:
Shear Stress (τ) = (Force (F) * Radius (r)) / (Area (A))
1. Calculate the radius of the spring:
The diameter of the steel wire is given as 10 mm, so the radius (r) is half of the diameter, which is 5 mm or 0.005 m.
2. Calculate the area of the spring:
The area (A) of the spring can be calculated using the formula for the area of a circle:
A = π * r^2
Substituting the value of radius, we get:
A = π * (0.005)^2 = 0.00007854 m^2
3. Calculate the axial force:
The axial pull on the spring is given as 200 N.
4. Calculate the shear stress:
Substituting the values into the formula for shear stress, we get:
τ = (200 * 0.005) / 0.00007854 = 12,762.67 N/m^2
However, the modulus of rigidity is given in kN/mm^2, so we need to convert the units:
τ = 12,762.67 N/m^2 * (1 kN / 1000 N) * (1000 mm / 1 m)^2 = 12.76267 N/mm^2
The value of shear stress induced in the spring is approximately 12.76 N/mm^2.
The given options are in N/mm^2. Comparing this value with the options, we find that option A, which is 61.1 N/mm^2 and 34.6 N/mm^2, is the closest.
Therefore, the correct answer is option A.
Shear Stress (τ) = (Force (F) * Radius (r)) / (Area (A))
1. Calculate the radius of the spring:
The diameter of the steel wire is given as 10 mm, so the radius (r) is half of the diameter, which is 5 mm or 0.005 m.
2. Calculate the area of the spring:
The area (A) of the spring can be calculated using the formula for the area of a circle:
A = π * r^2
Substituting the value of radius, we get:
A = π * (0.005)^2 = 0.00007854 m^2
3. Calculate the axial force:
The axial pull on the spring is given as 200 N.
4. Calculate the shear stress:
Substituting the values into the formula for shear stress, we get:
τ = (200 * 0.005) / 0.00007854 = 12,762.67 N/m^2
However, the modulus of rigidity is given in kN/mm^2, so we need to convert the units:
τ = 12,762.67 N/m^2 * (1 kN / 1000 N) * (1000 mm / 1 m)^2 = 12.76267 N/mm^2
The value of shear stress induced in the spring is approximately 12.76 N/mm^2.
The given options are in N/mm^2. Comparing this value with the options, we find that option A, which is 61.1 N/mm^2 and 34.6 N/mm^2, is the closest.
Therefore, the correct answer is option A.
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A closely-coiled helical spring is made of 10 mm diameter steel wire, with the coil consisting of 10 turns with a mean diameter 120 mm. The spring carries an axial pull of 200 N. What is the value of shear stress induced in the spring neglecting the effect of stress concentration and of deflection in the spring, when the modulus of rigidity is 80 kN/mm2? a) 61.1 N/mm2 and 34.6 N/mm2b) 54.2 N/mm2 and 34.6 N/mm2c) 63.5 N/mm2 and 42.6 N/mm2d) 54.2 N/mm2 and 42.6 N/mm2Correct answer is option 'A'. Can you explain this answer?
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A closely-coiled helical spring is made of 10 mm diameter steel wire, with the coil consisting of 10 turns with a mean diameter 120 mm. The spring carries an axial pull of 200 N. What is the value of shear stress induced in the spring neglecting the effect of stress concentration and of deflection in the spring, when the modulus of rigidity is 80 kN/mm2? a) 61.1 N/mm2 and 34.6 N/mm2b) 54.2 N/mm2 and 34.6 N/mm2c) 63.5 N/mm2 and 42.6 N/mm2d) 54.2 N/mm2 and 42.6 N/mm2Correct answer is option 'A'. 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 closely-coiled helical spring is made of 10 mm diameter steel wire, with the coil consisting of 10 turns with a mean diameter 120 mm. The spring carries an axial pull of 200 N. What is the value of shear stress induced in the spring neglecting the effect of stress concentration and of deflection in the spring, when the modulus of rigidity is 80 kN/mm2? a) 61.1 N/mm2 and 34.6 N/mm2b) 54.2 N/mm2 and 34.6 N/mm2c) 63.5 N/mm2 and 42.6 N/mm2d) 54.2 N/mm2 and 42.6 N/mm2Correct answer is option 'A'. 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 closely-coiled helical spring is made of 10 mm diameter steel wire, with the coil consisting of 10 turns with a mean diameter 120 mm. The spring carries an axial pull of 200 N. What is the value of shear stress induced in the spring neglecting the effect of stress concentration and of deflection in the spring, when the modulus of rigidity is 80 kN/mm2? a) 61.1 N/mm2 and 34.6 N/mm2b) 54.2 N/mm2 and 34.6 N/mm2c) 63.5 N/mm2 and 42.6 N/mm2d) 54.2 N/mm2 and 42.6 N/mm2Correct answer is option 'A'. Can you explain this answer?.
A closely-coiled helical spring is made of 10 mm diameter steel wire, with the coil consisting of 10 turns with a mean diameter 120 mm. The spring carries an axial pull of 200 N. What is the value of shear stress induced in the spring neglecting the effect of stress concentration and of deflection in the spring, when the modulus of rigidity is 80 kN/mm2? a) 61.1 N/mm2 and 34.6 N/mm2b) 54.2 N/mm2 and 34.6 N/mm2c) 63.5 N/mm2 and 42.6 N/mm2d) 54.2 N/mm2 and 42.6 N/mm2Correct answer is option 'A'. 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 closely-coiled helical spring is made of 10 mm diameter steel wire, with the coil consisting of 10 turns with a mean diameter 120 mm. The spring carries an axial pull of 200 N. What is the value of shear stress induced in the spring neglecting the effect of stress concentration and of deflection in the spring, when the modulus of rigidity is 80 kN/mm2? a) 61.1 N/mm2 and 34.6 N/mm2b) 54.2 N/mm2 and 34.6 N/mm2c) 63.5 N/mm2 and 42.6 N/mm2d) 54.2 N/mm2 and 42.6 N/mm2Correct answer is option 'A'. 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 closely-coiled helical spring is made of 10 mm diameter steel wire, with the coil consisting of 10 turns with a mean diameter 120 mm. The spring carries an axial pull of 200 N. What is the value of shear stress induced in the spring neglecting the effect of stress concentration and of deflection in the spring, when the modulus of rigidity is 80 kN/mm2? a) 61.1 N/mm2 and 34.6 N/mm2b) 54.2 N/mm2 and 34.6 N/mm2c) 63.5 N/mm2 and 42.6 N/mm2d) 54.2 N/mm2 and 42.6 N/mm2Correct answer is option 'A'. Can you explain this answer?.
Solutions for A closely-coiled helical spring is made of 10 mm diameter steel wire, with the coil consisting of 10 turns with a mean diameter 120 mm. The spring carries an axial pull of 200 N. What is the value of shear stress induced in the spring neglecting the effect of stress concentration and of deflection in the spring, when the modulus of rigidity is 80 kN/mm2? a) 61.1 N/mm2 and 34.6 N/mm2b) 54.2 N/mm2 and 34.6 N/mm2c) 63.5 N/mm2 and 42.6 N/mm2d) 54.2 N/mm2 and 42.6 N/mm2Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mechanical Engineering.
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A closely-coiled helical spring is made of 10 mm diameter steel wire, with the coil consisting of 10 turns with a mean diameter 120 mm. The spring carries an axial pull of 200 N. What is the value of shear stress induced in the spring neglecting the effect of stress concentration and of deflection in the spring, when the modulus of rigidity is 80 kN/mm2? a) 61.1 N/mm2 and 34.6 N/mm2b) 54.2 N/mm2 and 34.6 N/mm2c) 63.5 N/mm2 and 42.6 N/mm2d) 54.2 N/mm2 and 42.6 N/mm2Correct answer is option 'A'. Can you explain this answer?, a detailed solution for A closely-coiled helical spring is made of 10 mm diameter steel wire, with the coil consisting of 10 turns with a mean diameter 120 mm. The spring carries an axial pull of 200 N. What is the value of shear stress induced in the spring neglecting the effect of stress concentration and of deflection in the spring, when the modulus of rigidity is 80 kN/mm2? a) 61.1 N/mm2 and 34.6 N/mm2b) 54.2 N/mm2 and 34.6 N/mm2c) 63.5 N/mm2 and 42.6 N/mm2d) 54.2 N/mm2 and 42.6 N/mm2Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of A closely-coiled helical spring is made of 10 mm diameter steel wire, with the coil consisting of 10 turns with a mean diameter 120 mm. The spring carries an axial pull of 200 N. What is the value of shear stress induced in the spring neglecting the effect of stress concentration and of deflection in the spring, when the modulus of rigidity is 80 kN/mm2? a) 61.1 N/mm2 and 34.6 N/mm2b) 54.2 N/mm2 and 34.6 N/mm2c) 63.5 N/mm2 and 42.6 N/mm2d) 54.2 N/mm2 and 42.6 N/mm2Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A closely-coiled helical spring is made of 10 mm diameter steel wire, with the coil consisting of 10 turns with a mean diameter 120 mm. The spring carries an axial pull of 200 N. What is the value of shear stress induced in the spring neglecting the effect of stress concentration and of deflection in the spring, when the modulus of rigidity is 80 kN/mm2? a) 61.1 N/mm2 and 34.6 N/mm2b) 54.2 N/mm2 and 34.6 N/mm2c) 63.5 N/mm2 and 42.6 N/mm2d) 54.2 N/mm2 and 42.6 N/mm2Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice Mechanical Engineering tests.
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