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A pulley is connected to a power transmission shaft of diameter d by means of a rectangular sunk key of width wand length ‘l’. The width of the key is taken as d/4. For full power transmission, the shearing strength of the key is equal to the torsional shearing strength of the shaft. The ratio of the length of the key to the diameter of the shaft (l/d) is
- a)π/4
- b)π/√2
- c)π/2
- d)π
Correct answer is option 'C'. Can you explain this answer?
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To determine the ratio of the length of the key (l) to the diameter of the shaft (d), we need to compare the shearing strengths of the key and the shaft.
1. Shearing Strength of the Key:
The shearing strength of a rectangular sunk key can be calculated using the formula:
Shearing Strength of Key = (Width of Key * Length of Key * Shear Stress) / (Factor of Safety)
Given that the width of the key is d/4, we can substitute this value into the formula:
Shearing Strength of Key = ((d/4) * l * Shear Stress) / (Factor of Safety)
2. Shearing Strength of the Shaft:
The shearing strength of a shaft can be calculated using the formula:
Shearing Strength of Shaft = (π/16) * (d^3) * Shear Stress
3. Equating the Shearing Strengths:
Since the shearing strength of the key is equal to the shearing strength of the shaft for full power transmission, we can set the two equations equal to each other:
((d/4) * l * Shear Stress) / (Factor of Safety) = (π/16) * (d^3) * Shear Stress
4. Simplifying the Equation:
To simplify the equation, we can cancel out the shear stress terms:
(d/4) * l / (Factor of Safety) = (π/16) * (d^3)
5. Determining the Ratio (l/d):
To find the ratio of l/d, we can rearrange the equation:
l/d = (π/16) * (d^2) / ((d/4) * (Factor of Safety))
Simplifying further:
l/d = (4π/16) * (d^2) / (d * (Factor of Safety))
l/d = (π/4) * (d/Factor of Safety)
Since the width of the key is taken as d/4, we can substitute this value into the equation:
l/d = (π/4) * (Width of Key/Factor of Safety)
Therefore, the ratio of l/d is given by (π/4), which is equal to option 'C'.
1. Shearing Strength of the Key:
The shearing strength of a rectangular sunk key can be calculated using the formula:
Shearing Strength of Key = (Width of Key * Length of Key * Shear Stress) / (Factor of Safety)
Given that the width of the key is d/4, we can substitute this value into the formula:
Shearing Strength of Key = ((d/4) * l * Shear Stress) / (Factor of Safety)
2. Shearing Strength of the Shaft:
The shearing strength of a shaft can be calculated using the formula:
Shearing Strength of Shaft = (π/16) * (d^3) * Shear Stress
3. Equating the Shearing Strengths:
Since the shearing strength of the key is equal to the shearing strength of the shaft for full power transmission, we can set the two equations equal to each other:
((d/4) * l * Shear Stress) / (Factor of Safety) = (π/16) * (d^3) * Shear Stress
4. Simplifying the Equation:
To simplify the equation, we can cancel out the shear stress terms:
(d/4) * l / (Factor of Safety) = (π/16) * (d^3)
5. Determining the Ratio (l/d):
To find the ratio of l/d, we can rearrange the equation:
l/d = (π/16) * (d^2) / ((d/4) * (Factor of Safety))
Simplifying further:
l/d = (4π/16) * (d^2) / (d * (Factor of Safety))
l/d = (π/4) * (d/Factor of Safety)
Since the width of the key is taken as d/4, we can substitute this value into the equation:
l/d = (π/4) * (Width of Key/Factor of Safety)
Therefore, the ratio of l/d is given by (π/4), which is equal to option 'C'.
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A pulley is connected to a power transmission shaft of diameter d by means of a rectangular sunk key of width wand length ‘l’. The width of the key is taken as d/4. For full power transmission, the shearing strength of the key is equal to the torsional shearing strength of the shaft. The ratio of the length of the key to the diameter of the shaft (l/d) is a)π/4b)π/√2c)π/2d)πCorrect answer is option 'C'. Can you explain this answer?
Question Description
A pulley is connected to a power transmission shaft of diameter d by means of a rectangular sunk key of width wand length ‘l’. The width of the key is taken as d/4. For full power transmission, the shearing strength of the key is equal to the torsional shearing strength of the shaft. The ratio of the length of the key to the diameter of the shaft (l/d) is a)π/4b)π/√2c)π/2d)πCorrect 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 A pulley is connected to a power transmission shaft of diameter d by means of a rectangular sunk key of width wand length ‘l’. The width of the key is taken as d/4. For full power transmission, the shearing strength of the key is equal to the torsional shearing strength of the shaft. The ratio of the length of the key to the diameter of the shaft (l/d) is a)π/4b)π/√2c)π/2d)πCorrect 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 A pulley is connected to a power transmission shaft of diameter d by means of a rectangular sunk key of width wand length ‘l’. The width of the key is taken as d/4. For full power transmission, the shearing strength of the key is equal to the torsional shearing strength of the shaft. The ratio of the length of the key to the diameter of the shaft (l/d) is a)π/4b)π/√2c)π/2d)πCorrect answer is option 'C'. Can you explain this answer?.
A pulley is connected to a power transmission shaft of diameter d by means of a rectangular sunk key of width wand length ‘l’. The width of the key is taken as d/4. For full power transmission, the shearing strength of the key is equal to the torsional shearing strength of the shaft. The ratio of the length of the key to the diameter of the shaft (l/d) is a)π/4b)π/√2c)π/2d)πCorrect 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 A pulley is connected to a power transmission shaft of diameter d by means of a rectangular sunk key of width wand length ‘l’. The width of the key is taken as d/4. For full power transmission, the shearing strength of the key is equal to the torsional shearing strength of the shaft. The ratio of the length of the key to the diameter of the shaft (l/d) is a)π/4b)π/√2c)π/2d)πCorrect 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 A pulley is connected to a power transmission shaft of diameter d by means of a rectangular sunk key of width wand length ‘l’. The width of the key is taken as d/4. For full power transmission, the shearing strength of the key is equal to the torsional shearing strength of the shaft. The ratio of the length of the key to the diameter of the shaft (l/d) is a)π/4b)π/√2c)π/2d)πCorrect answer is option 'C'. Can you explain this answer?.
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