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A flywheel in a system is shifted to another shaft which rotates at double the speed of earlier one. The coefficient of fluctuation of speed compared to earlier case for the same fluctuation of energy is
- a)Same
- b)Doubled
- c)Reduce to 1/4
- d)Reduce to 1/2
Correct answer is option 'C'. Can you explain this answer?
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Given information:
- A flywheel in a system is shifted to another shaft.
- The new shaft rotates at double the speed of the earlier one.
Fluctuation of energy:
- Fluctuation of energy refers to the variation in the energy stored in a flywheel as it rotates.
- Fluctuation of energy can be caused by changes in speed or mass distribution of the flywheel.
Fluctuation of speed:
- Fluctuation of speed refers to the variation in the rotational speed of the flywheel.
- Fluctuation of speed can be caused by changes in the driving torque or load torque on the flywheel.
Coefficient of fluctuation of speed:
- The coefficient of fluctuation of speed is a measure of the relative change in speed of the flywheel.
- It is defined as the ratio of the maximum change in speed to the mean speed of the flywheel.
Comparison of coefficients of fluctuation of speed:
- In the given scenario, the flywheel is shifted to a new shaft that rotates at double the speed of the earlier one.
- Let's assume the coefficient of fluctuation of speed for the earlier case is 'k'.
- Since the new shaft rotates at double the speed, the mean speed of the flywheel is also doubled.
- Let's say the maximum change in speed for both cases is 'Δv'.
- The coefficient of fluctuation of speed for the new case can be calculated as follows:
Coefficient of fluctuation of speed for new case = (maximum change in speed for new case) / (mean speed for new case)
- The maximum change in speed for the new case is still 'Δv'.
- The mean speed for the new case is double the mean speed for the earlier case.
- Therefore, the coefficient of fluctuation of speed for the new case is:
Coefficient of fluctuation of speed for new case = Δv / (2 * mean speed for earlier case)
- Since the mean speed for the new case is double the mean speed for the earlier case, the coefficient of fluctuation of speed for the new case is halved compared to the earlier case.
- Therefore, the correct answer is option 'd', i.e., the coefficient of fluctuation of speed reduces to 1/2.
- A flywheel in a system is shifted to another shaft.
- The new shaft rotates at double the speed of the earlier one.
Fluctuation of energy:
- Fluctuation of energy refers to the variation in the energy stored in a flywheel as it rotates.
- Fluctuation of energy can be caused by changes in speed or mass distribution of the flywheel.
Fluctuation of speed:
- Fluctuation of speed refers to the variation in the rotational speed of the flywheel.
- Fluctuation of speed can be caused by changes in the driving torque or load torque on the flywheel.
Coefficient of fluctuation of speed:
- The coefficient of fluctuation of speed is a measure of the relative change in speed of the flywheel.
- It is defined as the ratio of the maximum change in speed to the mean speed of the flywheel.
Comparison of coefficients of fluctuation of speed:
- In the given scenario, the flywheel is shifted to a new shaft that rotates at double the speed of the earlier one.
- Let's assume the coefficient of fluctuation of speed for the earlier case is 'k'.
- Since the new shaft rotates at double the speed, the mean speed of the flywheel is also doubled.
- Let's say the maximum change in speed for both cases is 'Δv'.
- The coefficient of fluctuation of speed for the new case can be calculated as follows:
Coefficient of fluctuation of speed for new case = (maximum change in speed for new case) / (mean speed for new case)
- The maximum change in speed for the new case is still 'Δv'.
- The mean speed for the new case is double the mean speed for the earlier case.
- Therefore, the coefficient of fluctuation of speed for the new case is:
Coefficient of fluctuation of speed for new case = Δv / (2 * mean speed for earlier case)
- Since the mean speed for the new case is double the mean speed for the earlier case, the coefficient of fluctuation of speed for the new case is halved compared to the earlier case.
- Therefore, the correct answer is option 'd', i.e., the coefficient of fluctuation of speed reduces to 1/2.
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A flywheel in a system is shifted to another shaft which rotates at double the speed of earlier one. The coefficient of fluctuation of speed compared to earlier case for the same fluctuation of energy isa)Sameb)Doubledc)Reduce to 1/4d)Reduce to 1/2Correct answer is option 'C'. Can you explain this answer?
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