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A flywheel fitted to the steam engine has mass of 1000 kg. It’s radius of gyration is 400 mm. The starting torque of the engine is 580 Nm and is assumed to be constant. The kinetic energy of the flywheel after 14 sec is______ .
- a)205.04
- b)206.04
- c)207.05
- d)208.06
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A flywheel fitted to the steam engine has mass of 1000 kg. It’s radiu...
ω2 = ω1 + αt
ω2 = 0 + 3. 625 × 14
ω2 = 50. 75 rad/s
= 206045 J
= 206.045 kJ
Most Upvoted Answer
A flywheel fitted to the steam engine has mass of 1000 kg. It’s radiu...
The kinetic energy of a rotating object can be calculated using the formula:
K.E. = (1/2) * I * ω^2
Where:
K.E. = Kinetic energy
I = Moment of inertia
ω = Angular velocity
To solve this problem, we need to calculate the moment of inertia of the flywheel and the angular velocity after 14 seconds.
1. Moment of Inertia (I):
The moment of inertia of a flywheel can be calculated using the formula:
I = m * k^2
Where:
m = Mass of the flywheel
k = Radius of gyration
Given:
Mass of the flywheel (m) = 1000 kg
Radius of gyration (k) = 400 mm = 0.4 m
Substituting these values into the formula, we get:
I = 1000 kg * (0.4 m)^2
I = 160 kg * m^2
2. Angular Velocity (ω):
The angular velocity can be calculated using the formula:
ω = Δθ / Δt
Where:
Δθ = Change in angle
Δt = Change in time
Given:
Δθ = 2π (as the flywheel completes one full revolution)
Δt = 14 seconds
Substituting these values into the formula, we get:
ω = 2π / 14
ω = π / 7 rad/s
3. Kinetic Energy (K.E.):
Now, we can substitute the values of moment of inertia (I) and angular velocity (ω) into the formula for kinetic energy.
K.E. = (1/2) * I * ω^2
K.E. = (1/2) * 160 kg * m^2 * (π / 7 rad/s)^2
K.E. = (1/2) * 160 * (π / 7)^2 * kg * m^2 * rad^2/s^2
K.E. ≈ 206.04 J
Therefore, the kinetic energy of the flywheel after 14 seconds is approximately 206.04 J. Hence, the correct answer is option B.
K.E. = (1/2) * I * ω^2
Where:
K.E. = Kinetic energy
I = Moment of inertia
ω = Angular velocity
To solve this problem, we need to calculate the moment of inertia of the flywheel and the angular velocity after 14 seconds.
1. Moment of Inertia (I):
The moment of inertia of a flywheel can be calculated using the formula:
I = m * k^2
Where:
m = Mass of the flywheel
k = Radius of gyration
Given:
Mass of the flywheel (m) = 1000 kg
Radius of gyration (k) = 400 mm = 0.4 m
Substituting these values into the formula, we get:
I = 1000 kg * (0.4 m)^2
I = 160 kg * m^2
2. Angular Velocity (ω):
The angular velocity can be calculated using the formula:
ω = Δθ / Δt
Where:
Δθ = Change in angle
Δt = Change in time
Given:
Δθ = 2π (as the flywheel completes one full revolution)
Δt = 14 seconds
Substituting these values into the formula, we get:
ω = 2π / 14
ω = π / 7 rad/s
3. Kinetic Energy (K.E.):
Now, we can substitute the values of moment of inertia (I) and angular velocity (ω) into the formula for kinetic energy.
K.E. = (1/2) * I * ω^2
K.E. = (1/2) * 160 kg * m^2 * (π / 7 rad/s)^2
K.E. = (1/2) * 160 * (π / 7)^2 * kg * m^2 * rad^2/s^2
K.E. ≈ 206.04 J
Therefore, the kinetic energy of the flywheel after 14 seconds is approximately 206.04 J. Hence, the correct answer is option B.
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A flywheel fitted to the steam engine has mass of 1000 kg. It’s radius of gyration is 400 mm. The starting torque of the engine is 580 Nm and is assumed to be constant. The kinetic energy of the flywheel after 14 sec is______ .a)205.04b)206.04c)207.05d)208.06Correct answer is option 'B'. Can you explain this answer?
Question Description
A flywheel fitted to the steam engine has mass of 1000 kg. It’s radius of gyration is 400 mm. The starting torque of the engine is 580 Nm and is assumed to be constant. The kinetic energy of the flywheel after 14 sec is______ .a)205.04b)206.04c)207.05d)208.06Correct answer is option 'B'. 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 fitted to the steam engine has mass of 1000 kg. It’s radius of gyration is 400 mm. The starting torque of the engine is 580 Nm and is assumed to be constant. The kinetic energy of the flywheel after 14 sec is______ .a)205.04b)206.04c)207.05d)208.06Correct answer is option 'B'. 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 fitted to the steam engine has mass of 1000 kg. It’s radius of gyration is 400 mm. The starting torque of the engine is 580 Nm and is assumed to be constant. The kinetic energy of the flywheel after 14 sec is______ .a)205.04b)206.04c)207.05d)208.06Correct answer is option 'B'. Can you explain this answer?.
A flywheel fitted to the steam engine has mass of 1000 kg. It’s radius of gyration is 400 mm. The starting torque of the engine is 580 Nm and is assumed to be constant. The kinetic energy of the flywheel after 14 sec is______ .a)205.04b)206.04c)207.05d)208.06Correct answer is option 'B'. 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 fitted to the steam engine has mass of 1000 kg. It’s radius of gyration is 400 mm. The starting torque of the engine is 580 Nm and is assumed to be constant. The kinetic energy of the flywheel after 14 sec is______ .a)205.04b)206.04c)207.05d)208.06Correct answer is option 'B'. 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 fitted to the steam engine has mass of 1000 kg. It’s radius of gyration is 400 mm. The starting torque of the engine is 580 Nm and is assumed to be constant. The kinetic energy of the flywheel after 14 sec is______ .a)205.04b)206.04c)207.05d)208.06Correct answer is option 'B'. Can you explain this answer?.
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A flywheel fitted to the steam engine has mass of 1000 kg. It’s radius of gyration is 400 mm. The starting torque of the engine is 580 Nm and is assumed to be constant. The kinetic energy of the flywheel after 14 sec is______ .a)205.04b)206.04c)207.05d)208.06Correct answer is option 'B'. Can you explain this answer?, a detailed solution for A flywheel fitted to the steam engine has mass of 1000 kg. It’s radius of gyration is 400 mm. The starting torque of the engine is 580 Nm and is assumed to be constant. The kinetic energy of the flywheel after 14 sec is______ .a)205.04b)206.04c)207.05d)208.06Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of A flywheel fitted to the steam engine has mass of 1000 kg. It’s radius of gyration is 400 mm. The starting torque of the engine is 580 Nm and is assumed to be constant. The kinetic energy of the flywheel after 14 sec is______ .a)205.04b)206.04c)207.05d)208.06Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
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