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The diameter of shaft A is twice the diameter of shaft B and both are made of the same material. Assuming both the shafts to rotate at the same speed, the maximum power transmitted by B is
- a)The same as that of A
- b)Half of A
- c)1/8th of A
- d)1/4th of A
Correct answer is option 'C'. Can you explain this answer?
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Shaft A and Shaft B
- Shaft A has a diameter twice that of Shaft B.
- Both shafts are made of the same material.
- Both shafts rotate at the same speed.
Power Transmitted
The power transmitted by a rotating shaft is given by the equation:
Power (P) = (Torque (T) × Angular velocity (ω)) / 1000
Here, torque is the force applied perpendicular to the shaft multiplied by the radius of the shaft, and angular velocity is the rate at which the shaft rotates.
Comparison of Shafts A and B
Since both shafts are rotating at the same speed, the angular velocity (ω) is the same for both.
Let the diameter of Shaft B be D, then the diameter of Shaft A is 2D.
The radius of Shaft B is D/2, and the radius of Shaft A is (2D)/2 = D.
Torque Calculation
The torque transmitted by a shaft is directly proportional to the radius of the shaft.
Since both shafts are made of the same material, the torque transmitted by Shaft A is directly proportional to the radius of Shaft A, and the torque transmitted by Shaft B is directly proportional to the radius of Shaft B.
Hence, the torque transmitted by Shaft A is 2 times the torque transmitted by Shaft B.
Power Calculation
Using the equation for power, we have:
Power (A) = (Torque (A) × Angular velocity (ω)) / 1000
Power (B) = (Torque (B) × Angular velocity (ω)) / 1000
Since the angular velocity is the same for both shafts, it can be canceled out.
Therefore, Power (A) = Torque (A) / 1000
Power (B) = Torque (B) / 1000
Substituting the torque values, we have:
Power (A) = (2 × Torque (B)) / 1000
Since the torque transmitted by Shaft A is 2 times the torque transmitted by Shaft B, we can rewrite the equation as:
Power (A) = (2 × 2 × Torque (B)) / 1000
Power (A) = (4 × Torque (B)) / 1000
This means that the power transmitted by Shaft A is 4 times the power transmitted by Shaft B.
Conclusion
Hence, the maximum power transmitted by Shaft B is 1/4th of the power transmitted by Shaft A. Therefore, the correct answer is option 'd', 1/4th of A.
- Shaft A has a diameter twice that of Shaft B.
- Both shafts are made of the same material.
- Both shafts rotate at the same speed.
Power Transmitted
The power transmitted by a rotating shaft is given by the equation:
Power (P) = (Torque (T) × Angular velocity (ω)) / 1000
Here, torque is the force applied perpendicular to the shaft multiplied by the radius of the shaft, and angular velocity is the rate at which the shaft rotates.
Comparison of Shafts A and B
Since both shafts are rotating at the same speed, the angular velocity (ω) is the same for both.
Let the diameter of Shaft B be D, then the diameter of Shaft A is 2D.
The radius of Shaft B is D/2, and the radius of Shaft A is (2D)/2 = D.
Torque Calculation
The torque transmitted by a shaft is directly proportional to the radius of the shaft.
Since both shafts are made of the same material, the torque transmitted by Shaft A is directly proportional to the radius of Shaft A, and the torque transmitted by Shaft B is directly proportional to the radius of Shaft B.
Hence, the torque transmitted by Shaft A is 2 times the torque transmitted by Shaft B.
Power Calculation
Using the equation for power, we have:
Power (A) = (Torque (A) × Angular velocity (ω)) / 1000
Power (B) = (Torque (B) × Angular velocity (ω)) / 1000
Since the angular velocity is the same for both shafts, it can be canceled out.
Therefore, Power (A) = Torque (A) / 1000
Power (B) = Torque (B) / 1000
Substituting the torque values, we have:
Power (A) = (2 × Torque (B)) / 1000
Since the torque transmitted by Shaft A is 2 times the torque transmitted by Shaft B, we can rewrite the equation as:
Power (A) = (2 × 2 × Torque (B)) / 1000
Power (A) = (4 × Torque (B)) / 1000
This means that the power transmitted by Shaft A is 4 times the power transmitted by Shaft B.
Conclusion
Hence, the maximum power transmitted by Shaft B is 1/4th of the power transmitted by Shaft A. Therefore, the correct answer is option 'd', 1/4th of A.
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The diameter of shaft A is twice the diameter of shaft B and both are made of the same material. Assuming both the shafts to rotate at the same speed, the maximum power transmitted by B isa)The same as that of Ab)Half of Ac)1/8thof Ad)1/4thof ACorrect answer is option 'C'. Can you explain this answer?
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