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A hollow shaft having an inside diameter 60% of its outside diameter is to replace a solid shaft transmitting the same power at the same speed. If the material is the same, the percentage saving in the materials is
- a)29.84%
- b)30.25%
- c)15%
- d)18.2%
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A hollow shaft having an inside diameter 60% of its outside diameter ...
Torque transmitted by solid shaft
View all questions of this test
T = 
Torque transmitted by hollow shaft
T = 
= 
= 
Torque transmitted is the same equate ① and ②
D = 0.9548 D0
Area of solid shaft. As = 
= 0.716 D02
Area of hollow shaft,
AH = 
= 
= 0.502 D02
For the same material, the weight of the shaft is proportional to the areas Saving in material = saving in area
= 
= 
= 29.88%
Most Upvoted Answer
A hollow shaft having an inside diameter 60% of its outside diameter ...
Given:
Inside diameter of hollow shaft = 0.6 × Outside diameter of hollow shaft
Material of solid shaft and hollow shaft is same
Both the shafts transmit same power at same speed
To find:
Percentage saving in the materials
Solution:
Let,
D = Outside diameter of solid shaft
d = Inside diameter of hollow shaft
P = Power transmitted by both the shafts
N = Speed of both the shafts
ρ = Density of material of both the shafts
T = Torque transmitted by both the shafts
Power transmitted by solid shaft = P = 2πNT
Power transmitted by hollow shaft = P = 2πNT
Torque transmitted by solid shaft = T = (π/16)ρD^3
Torque transmitted by hollow shaft = T = (π/16)ρ(D^4 - d^4)/D
Since both the shafts transmit same power at same speed, we can equate the torque equations:
(π/16)ρD^3 = (π/16)ρ(D^4 - d^4)/D
D^4 - d^4 = D^4/4
3D^4/4 = d^4
d/D = (3/4)^(1/4)
Percentage saving in material = (Volume of solid shaft - Volume of hollow shaft)/Volume of solid shaft × 100%
Volume of solid shaft = (π/4)D^2(4D/4)
Volume of hollow shaft = (π/4)(D^2 - d^2)(4D/4)
= (π/4)D^2(1 - (3/4)^(1/2))(4/4)
Percentage saving in material = [(π/4)D^2(4 - 4(1 - (3/4)^(1/2)))/((π/4)D^2(4))] × 100%
= [4(3/4)^(1/2)] × 100%
= 29.84%
Therefore, the percentage saving in the materials is 29.84% (option A).
Inside diameter of hollow shaft = 0.6 × Outside diameter of hollow shaft
Material of solid shaft and hollow shaft is same
Both the shafts transmit same power at same speed
To find:
Percentage saving in the materials
Solution:
Let,
D = Outside diameter of solid shaft
d = Inside diameter of hollow shaft
P = Power transmitted by both the shafts
N = Speed of both the shafts
ρ = Density of material of both the shafts
T = Torque transmitted by both the shafts
Power transmitted by solid shaft = P = 2πNT
Power transmitted by hollow shaft = P = 2πNT
Torque transmitted by solid shaft = T = (π/16)ρD^3
Torque transmitted by hollow shaft = T = (π/16)ρ(D^4 - d^4)/D
Since both the shafts transmit same power at same speed, we can equate the torque equations:
(π/16)ρD^3 = (π/16)ρ(D^4 - d^4)/D
D^4 - d^4 = D^4/4
3D^4/4 = d^4
d/D = (3/4)^(1/4)
Percentage saving in material = (Volume of solid shaft - Volume of hollow shaft)/Volume of solid shaft × 100%
Volume of solid shaft = (π/4)D^2(4D/4)
Volume of hollow shaft = (π/4)(D^2 - d^2)(4D/4)
= (π/4)D^2(1 - (3/4)^(1/2))(4/4)
Percentage saving in material = [(π/4)D^2(4 - 4(1 - (3/4)^(1/2)))/((π/4)D^2(4))] × 100%
= [4(3/4)^(1/2)] × 100%
= 29.84%
Therefore, the percentage saving in the materials is 29.84% (option A).
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A hollow shaft having an inside diameter 60% of its outside diameter is to replace a solid shaft transmitting the same power at the same speed. If the material is the same, the percentage saving in the materials isa)29.84%b) 30.25%c) 15%d) 18.2%Correct answer is option 'A'. Can you explain this answer?
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A hollow shaft having an inside diameter 60% of its outside diameter is to replace a solid shaft transmitting the same power at the same speed. If the material is the same, the percentage saving in the materials isa)29.84%b) 30.25%c) 15%d) 18.2%Correct 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 hollow shaft having an inside diameter 60% of its outside diameter is to replace a solid shaft transmitting the same power at the same speed. If the material is the same, the percentage saving in the materials isa)29.84%b) 30.25%c) 15%d) 18.2%Correct 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 hollow shaft having an inside diameter 60% of its outside diameter is to replace a solid shaft transmitting the same power at the same speed. If the material is the same, the percentage saving in the materials isa)29.84%b) 30.25%c) 15%d) 18.2%Correct answer is option 'A'. Can you explain this answer?.
A hollow shaft having an inside diameter 60% of its outside diameter is to replace a solid shaft transmitting the same power at the same speed. If the material is the same, the percentage saving in the materials isa)29.84%b) 30.25%c) 15%d) 18.2%Correct 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 hollow shaft having an inside diameter 60% of its outside diameter is to replace a solid shaft transmitting the same power at the same speed. If the material is the same, the percentage saving in the materials isa)29.84%b) 30.25%c) 15%d) 18.2%Correct 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 hollow shaft having an inside diameter 60% of its outside diameter is to replace a solid shaft transmitting the same power at the same speed. If the material is the same, the percentage saving in the materials isa)29.84%b) 30.25%c) 15%d) 18.2%Correct answer is option 'A'. Can you explain this answer?.
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