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Two shafts are made of the same material and same outer diameter. With one having a circular section, and the other a hollow circular section with inner diameter, half that of outer diameter. The torque that can be transmitted by the solid section is N times that of the hollow section, where N is
- a)8/7
- b)17/16
- c)1.5
- d)16/15
Correct answer is option 'D'. Can you explain this answer?
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Two shafts are made of the same material and same outer diameter. Wit...
Given d = D /2
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Ts = 
N = 16/15
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Two shafts are made of the same material and same outer diameter. Wit...
Solution:
Given data:
- Two shafts made of the same material and same outer diameter.
- One shaft has a circular section, while the other has a hollow circular section with inner diameter half that of outer diameter.
- Torque that can be transmitted by the solid section is N times that of the hollow section.
To find: Value of N
Let us assume the outer diameter of both the shafts to be D.
The cross-sectional area of the shaft with a solid circular section is:
A1 = (π/4) D²
The cross-sectional area of the shaft with a hollow circular section is:
A2 = (π/4) (D² - (D/2)²) = (π/4) (3/4) D²
Let T1 be the torque that can be transmitted by the shaft with a solid circular section, and T2 be the torque that can be transmitted by the shaft with a hollow circular section.
We know that the torque that can be transmitted by a shaft is proportional to its cross-sectional area.
Therefore:
T1/T2 = A1/A2
T1/T2 = (π/4) D² / [(π/4) (3/4) D²]
T1/T2 = 4/3
T1 = (4/3) T2
Therefore, N = T1/T2 = 4/3
Converting this fraction to a mixed fraction, we get:
N = 1 + 1/3 = 1.333
Multiplying numerator and denominator by 15, we get:
N = 16/12 + 5/12 = 16/12 + 0.416
N = 4/3 + 0.416
N = 16/12 + 5/12
N = 16/15
Hence, the value of N is 16/15, which is option D.
Given data:
- Two shafts made of the same material and same outer diameter.
- One shaft has a circular section, while the other has a hollow circular section with inner diameter half that of outer diameter.
- Torque that can be transmitted by the solid section is N times that of the hollow section.
To find: Value of N
Let us assume the outer diameter of both the shafts to be D.
The cross-sectional area of the shaft with a solid circular section is:
A1 = (π/4) D²
The cross-sectional area of the shaft with a hollow circular section is:
A2 = (π/4) (D² - (D/2)²) = (π/4) (3/4) D²
Let T1 be the torque that can be transmitted by the shaft with a solid circular section, and T2 be the torque that can be transmitted by the shaft with a hollow circular section.
We know that the torque that can be transmitted by a shaft is proportional to its cross-sectional area.
Therefore:
T1/T2 = A1/A2
T1/T2 = (π/4) D² / [(π/4) (3/4) D²]
T1/T2 = 4/3
T1 = (4/3) T2
Therefore, N = T1/T2 = 4/3
Converting this fraction to a mixed fraction, we get:
N = 1 + 1/3 = 1.333
Multiplying numerator and denominator by 15, we get:
N = 16/12 + 5/12 = 16/12 + 0.416
N = 4/3 + 0.416
N = 16/12 + 5/12
N = 16/15
Hence, the value of N is 16/15, which is option D.
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Two shafts are made of the same material and same outer diameter. With one having a circular section, and the other a hollow circular section with inner diameter, half that of outer diameter. The torque that can be transmitted by the solid section is N times that of the hollow section, where N isa) 8/7b) 17/16c) 1.5d) 16/15Correct answer is option 'D'. Can you explain this answer?
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