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A flywheel connected to a punching machine has to supply energy of 400 Nm while running at a mean angular speed of 20 radians/s. If the total fluctuation of speed is not to exceed ±2%, the mass moment of inertia of the flywheel in kg − m2 is
- a)25
- b)50
- c)100
- d)125
Correct answer is option 'A'. Can you explain this answer?
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2 radians/s, what should be the moment of inertia of the flywheel?
We can use the formula for the kinetic energy of a rotating object:
KE = (1/2) Iω^2
where KE is the kinetic energy, I is the moment of inertia, and ω is the angular speed.
We know that the energy to be supplied by the flywheel is 400 Nm, and the mean angular speed is 20 radians/s. Therefore, the kinetic energy of the flywheel is:
KE = 400 Nm
We also know that the total fluctuation of speed should not exceed 2 radians/s. This means that the minimum and maximum angular speeds are:
ω_min = 20 - 1 = 19 radians/s
ω_max = 20 + 1 = 21 radians/s
Using the formula for the kinetic energy, we can solve for the moment of inertia:
KE = (1/2) Iω^2
400 Nm = (1/2) I (19 radians/s)^2
400 Nm = (1/2) I (21 radians/s)^2
Solving for I, we get:
I = 105.26 kg m^2
Therefore, the moment of inertia of the flywheel should be 105.26 kg m^2 to ensure that the total fluctuation of speed does not exceed 2 radians/s.
We can use the formula for the kinetic energy of a rotating object:
KE = (1/2) Iω^2
where KE is the kinetic energy, I is the moment of inertia, and ω is the angular speed.
We know that the energy to be supplied by the flywheel is 400 Nm, and the mean angular speed is 20 radians/s. Therefore, the kinetic energy of the flywheel is:
KE = 400 Nm
We also know that the total fluctuation of speed should not exceed 2 radians/s. This means that the minimum and maximum angular speeds are:
ω_min = 20 - 1 = 19 radians/s
ω_max = 20 + 1 = 21 radians/s
Using the formula for the kinetic energy, we can solve for the moment of inertia:
KE = (1/2) Iω^2
400 Nm = (1/2) I (19 radians/s)^2
400 Nm = (1/2) I (21 radians/s)^2
Solving for I, we get:
I = 105.26 kg m^2
Therefore, the moment of inertia of the flywheel should be 105.26 kg m^2 to ensure that the total fluctuation of speed does not exceed 2 radians/s.
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A flywheel connected to a punching machine has to supply energy of 400 Nm while running at a mean angular speed of 20 radians/s. If the total fluctuation ofspeed is not to exceed ±2%, the mass moment of inertia of the flywheel inkg − m2 isa)25b)50c)100d)125Correct answer is option 'A'. Can you explain this answer?
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A flywheel connected to a punching machine has to supply energy of 400 Nm while running at a mean angular speed of 20 radians/s. If the total fluctuation ofspeed is not to exceed ±2%, the mass moment of inertia of the flywheel inkg − m2 isa)25b)50c)100d)125Correct answer is option 'A'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A flywheel connected to a punching machine has to supply energy of 400 Nm while running at a mean angular speed of 20 radians/s. If the total fluctuation ofspeed is not to exceed ±2%, the mass moment of inertia of the flywheel inkg − m2 isa)25b)50c)100d)125Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A flywheel connected to a punching machine has to supply energy of 400 Nm while running at a mean angular speed of 20 radians/s. If the total fluctuation ofspeed is not to exceed ±2%, the mass moment of inertia of the flywheel inkg − m2 isa)25b)50c)100d)125Correct answer is option 'A'. Can you explain this answer?.
A flywheel connected to a punching machine has to supply energy of 400 Nm while running at a mean angular speed of 20 radians/s. If the total fluctuation ofspeed is not to exceed ±2%, the mass moment of inertia of the flywheel inkg − m2 isa)25b)50c)100d)125Correct answer is option 'A'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A flywheel connected to a punching machine has to supply energy of 400 Nm while running at a mean angular speed of 20 radians/s. If the total fluctuation ofspeed is not to exceed ±2%, the mass moment of inertia of the flywheel inkg − m2 isa)25b)50c)100d)125Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A flywheel connected to a punching machine has to supply energy of 400 Nm while running at a mean angular speed of 20 radians/s. If the total fluctuation ofspeed is not to exceed ±2%, the mass moment of inertia of the flywheel inkg − m2 isa)25b)50c)100d)125Correct answer is option 'A'. Can you explain this answer?.
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