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A solid shaft of 200mm diameter has the same cross-sectional area as that of hollow shaft of same material with inside diameter of 150mm. Find ratio of power transmitted by two shafts at same speed.
- a)1.2
- b)3.4
- c)1.7
- d)2.4
Correct answer is option 'C'. Can you explain this answer?
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A solid shaft of 200mm diameterhas the same cross-sectional area astha...
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Given:
Diameter of solid shaft (D) = 200 mm
Inside diameter of hollow shaft (d) = 150 mm
Cross-sectional area of solid shaft = Cross-sectional area of hollow shaft
To find: Ratio of power transmitted by two shafts at same speed.
Solution:
Let's assume the length of both shafts as 'L' and the speed of both shafts as 'N'.
Cross-sectional area of solid shaft = πD²/4
Cross-sectional area of hollow shaft = π/4(D² - d²)
As given, both cross-sectional areas are equal.
πD²/4 = π/4(D² - d²)
On simplifying the above equation, we get
4D² - 4d² = D²
3D² = 4d²
D/d = √(4/3)
The ratio of power transmitted is directly proportional to (D/d)^4.
Ratio of power transmitted = (D/d)^4 = (4/3)^2 = 1.77 ≈ 1.7 (Option C)
Therefore, the correct answer is option C.
Diameter of solid shaft (D) = 200 mm
Inside diameter of hollow shaft (d) = 150 mm
Cross-sectional area of solid shaft = Cross-sectional area of hollow shaft
To find: Ratio of power transmitted by two shafts at same speed.
Solution:
Let's assume the length of both shafts as 'L' and the speed of both shafts as 'N'.
Cross-sectional area of solid shaft = πD²/4
Cross-sectional area of hollow shaft = π/4(D² - d²)
As given, both cross-sectional areas are equal.
πD²/4 = π/4(D² - d²)
On simplifying the above equation, we get
4D² - 4d² = D²
3D² = 4d²
D/d = √(4/3)
The ratio of power transmitted is directly proportional to (D/d)^4.
Ratio of power transmitted = (D/d)^4 = (4/3)^2 = 1.77 ≈ 1.7 (Option C)
Therefore, the correct answer is option C.
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A solid shaft of 200mm diameterhas the same cross-sectional area asthat of hollow shaft of samematerial with inside diameter of150mm. Find ratio of powertransmitted by two shafts at samespeed.a)1.2b)3.4c)1.7d)2.4Correct answer is option 'C'. Can you explain this answer?
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