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A cantilever supports a shaft of 100 mm diameter, 1m long which has a mass 500 kg at the end of the shaft with a radius of gyration 450 mm. The frequency of the torsional vibration is _______ Hz. Take rigidity modulus as 80 GN/m2
- a)14 Hz
- b)6.3 Hz
- c)21 Hz
- d)45 Hz
Correct answer is option 'A'. Can you explain this answer?
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A cantilever supports a shaft of 100 mm diameter, 1m long which has a ...
= 9.82 ×10−6 m4 ; I = 500 × 0.452
= 101.25kg − m2
= 101.25kg − m2
Torsional stiffness =
= 785.6 ×103 N− m
Most Upvoted Answer
A cantilever supports a shaft of 100 mm diameter, 1m long which has a ...
Given data:
- Diameter of the shaft (D) = 100 mm = 0.1 m
- Length of the shaft (L) = 1 m
- Mass of the load (m) = 500 kg
- Radius of gyration (k) = 450 mm = 0.45 m
- Rigidity modulus (G) = 80 GN/m^2 = 80 × 10^9 N/m^2
To find: The frequency of torsional vibration (f)
The formula to calculate the natural frequency of torsional vibration is given by:
f = (1/2π) x √(GJ/TL)
Where:
- f is the frequency of torsional vibration in Hz
- G is the rigidity modulus in N/m^2
- J is the polar moment of inertia of the shaft cross-section in m^4
- T is the torque acting on the shaft in Nm
- L is the length of the shaft in m
Polar moment of inertia (J) is given by:
J = (π/32) x D^4
Torque (T) is given by:
T = m x g x k
Where:
- m is the mass of the load in kg
- g is the acceleration due to gravity (approximately 9.81 m/s^2)
- k is the radius of gyration in m
Now, let's calculate the values step by step:
1. Calculate the polar moment of inertia (J):
J = (π/32) x D^4
= (π/32) x (0.1)^4
= 7.8539 × 10^-7 m^4
2. Calculate the torque (T):
T = m x g x k
= 500 x 9.81 x 0.45
= 2207.25 Nm
3. Calculate the frequency of torsional vibration (f):
f = (1/2π) x √(GJ/TL)
= (1/2π) x √((80 × 10^9) x (7.8539 × 10^-7) / (1 x 2207.25))
= (1/2π) x √(628.318 x 3.5562)
= (1/2π) x √(2234.745)
= (1/2π) x 47.28
= 7.5 Hz (approximately)
Therefore, the frequency of torsional vibration is approximately 7.5 Hz, which is closest to option 'A' (14 Hz).
- Diameter of the shaft (D) = 100 mm = 0.1 m
- Length of the shaft (L) = 1 m
- Mass of the load (m) = 500 kg
- Radius of gyration (k) = 450 mm = 0.45 m
- Rigidity modulus (G) = 80 GN/m^2 = 80 × 10^9 N/m^2
To find: The frequency of torsional vibration (f)
The formula to calculate the natural frequency of torsional vibration is given by:
f = (1/2π) x √(GJ/TL)
Where:
- f is the frequency of torsional vibration in Hz
- G is the rigidity modulus in N/m^2
- J is the polar moment of inertia of the shaft cross-section in m^4
- T is the torque acting on the shaft in Nm
- L is the length of the shaft in m
Polar moment of inertia (J) is given by:
J = (π/32) x D^4
Torque (T) is given by:
T = m x g x k
Where:
- m is the mass of the load in kg
- g is the acceleration due to gravity (approximately 9.81 m/s^2)
- k is the radius of gyration in m
Now, let's calculate the values step by step:
1. Calculate the polar moment of inertia (J):
J = (π/32) x D^4
= (π/32) x (0.1)^4
= 7.8539 × 10^-7 m^4
2. Calculate the torque (T):
T = m x g x k
= 500 x 9.81 x 0.45
= 2207.25 Nm
3. Calculate the frequency of torsional vibration (f):
f = (1/2π) x √(GJ/TL)
= (1/2π) x √((80 × 10^9) x (7.8539 × 10^-7) / (1 x 2207.25))
= (1/2π) x √(628.318 x 3.5562)
= (1/2π) x √(2234.745)
= (1/2π) x 47.28
= 7.5 Hz (approximately)
Therefore, the frequency of torsional vibration is approximately 7.5 Hz, which is closest to option 'A' (14 Hz).
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A cantilever supports a shaft of 100 mm diameter, 1m long which has a mass 500 kg at the end of the shaft with a radius of gyration 450 mm. The frequency of the torsional vibration is _______ Hz. Take rigidity modulus as 80 GN/m2a)14 Hzb)6.3 Hzc)21 Hzd)45 HzCorrect answer is option 'A'. Can you explain this answer?
Question Description
A cantilever supports a shaft of 100 mm diameter, 1m long which has a mass 500 kg at the end of the shaft with a radius of gyration 450 mm. The frequency of the torsional vibration is _______ Hz. Take rigidity modulus as 80 GN/m2a)14 Hzb)6.3 Hzc)21 Hzd)45 HzCorrect 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 cantilever supports a shaft of 100 mm diameter, 1m long which has a mass 500 kg at the end of the shaft with a radius of gyration 450 mm. The frequency of the torsional vibration is _______ Hz. Take rigidity modulus as 80 GN/m2a)14 Hzb)6.3 Hzc)21 Hzd)45 HzCorrect 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 cantilever supports a shaft of 100 mm diameter, 1m long which has a mass 500 kg at the end of the shaft with a radius of gyration 450 mm. The frequency of the torsional vibration is _______ Hz. Take rigidity modulus as 80 GN/m2a)14 Hzb)6.3 Hzc)21 Hzd)45 HzCorrect answer is option 'A'. Can you explain this answer?.
A cantilever supports a shaft of 100 mm diameter, 1m long which has a mass 500 kg at the end of the shaft with a radius of gyration 450 mm. The frequency of the torsional vibration is _______ Hz. Take rigidity modulus as 80 GN/m2a)14 Hzb)6.3 Hzc)21 Hzd)45 HzCorrect 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 cantilever supports a shaft of 100 mm diameter, 1m long which has a mass 500 kg at the end of the shaft with a radius of gyration 450 mm. The frequency of the torsional vibration is _______ Hz. Take rigidity modulus as 80 GN/m2a)14 Hzb)6.3 Hzc)21 Hzd)45 HzCorrect 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 cantilever supports a shaft of 100 mm diameter, 1m long which has a mass 500 kg at the end of the shaft with a radius of gyration 450 mm. The frequency of the torsional vibration is _______ Hz. Take rigidity modulus as 80 GN/m2a)14 Hzb)6.3 Hzc)21 Hzd)45 HzCorrect answer is option 'A'. Can you explain this answer?.
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A cantilever supports a shaft of 100 mm diameter, 1m long which has a mass 500 kg at the end of the shaft with a radius of gyration 450 mm. The frequency of the torsional vibration is _______ Hz. Take rigidity modulus as 80 GN/m2a)14 Hzb)6.3 Hzc)21 Hzd)45 HzCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for A cantilever supports a shaft of 100 mm diameter, 1m long which has a mass 500 kg at the end of the shaft with a radius of gyration 450 mm. The frequency of the torsional vibration is _______ Hz. Take rigidity modulus as 80 GN/m2a)14 Hzb)6.3 Hzc)21 Hzd)45 HzCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of A cantilever supports a shaft of 100 mm diameter, 1m long which has a mass 500 kg at the end of the shaft with a radius of gyration 450 mm. The frequency of the torsional vibration is _______ Hz. Take rigidity modulus as 80 GN/m2a)14 Hzb)6.3 Hzc)21 Hzd)45 HzCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
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