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During rotation the diameter of a flywheel increases by 1% the percent increases in its moment of inertia about the central axis is 1) 1 %. 2 )% 3 ) % 4)0.5%?
Most Upvoted Answer
During rotation the diameter of a flywheel increases by 1% the percent...
Wheel is like ring
moment of inertia = (m)(r)(r)
lets take radius 100 unit(R1)
radius after 1% increment= 101 unit (R2)
ration of new moment of inertia to the old one
= m(101)(101)/m(100)(100)= 10201/10000
which is approximately equal to 102/100
so u can se it increases by 2%
moment of inertia = (m)(r)(r)
lets take radius 100 unit(R1)
radius after 1% increment= 101 unit (R2)
ration of new moment of inertia to the old one
= m(101)(101)/m(100)(100)= 10201/10000
which is approximately equal to 102/100
so u can se it increases by 2%
Community Answer
During rotation the diameter of a flywheel increases by 1% the percent...
Explanation:
To understand the change in moment of inertia during rotation, we need to consider the formula for moment of inertia of a flywheel:
Moment of Inertia (I) = (1/2) * m * r^2
where m is the mass of the flywheel and r is the radius of the flywheel.
Change in Diameter:
Given that the diameter of the flywheel increases by 1%, we can calculate the change in radius using the formula:
Change in Radius = (Change in Diameter / 2)
Since the diameter increases by 1%, the change in diameter is 0.01 times the original diameter. Therefore, the change in radius is:
Change in Radius = (0.01 / 2) * Original Radius = 0.005 * Original Radius
Change in Moment of Inertia:
To find the change in moment of inertia, we need to consider the formula:
Change in Moment of Inertia = (1/2) * m * (Change in Radius)^2
Since the mass of the flywheel remains constant, we can ignore it in our calculations.
Change in Moment of Inertia = (1/2) * (Change in Radius)^2
Substituting the value of the change in radius, we get:
Change in Moment of Inertia = (1/2) * (0.005 * Original Radius)^2 = (1/2) * (0.000025) * (Original Radius)^2
Simplifying further, we find:
Change in Moment of Inertia = 0.0000125 * (Original Radius)^2
Answer:
From the above calculation, we can conclude that the percent increase in the moment of inertia about the central axis is 0.00125%, which is equivalent to 0.5% (option 4).
Therefore, the correct answer is option 4) 0.5%.
To understand the change in moment of inertia during rotation, we need to consider the formula for moment of inertia of a flywheel:
Moment of Inertia (I) = (1/2) * m * r^2
where m is the mass of the flywheel and r is the radius of the flywheel.
Change in Diameter:
Given that the diameter of the flywheel increases by 1%, we can calculate the change in radius using the formula:
Change in Radius = (Change in Diameter / 2)
Since the diameter increases by 1%, the change in diameter is 0.01 times the original diameter. Therefore, the change in radius is:
Change in Radius = (0.01 / 2) * Original Radius = 0.005 * Original Radius
Change in Moment of Inertia:
To find the change in moment of inertia, we need to consider the formula:
Change in Moment of Inertia = (1/2) * m * (Change in Radius)^2
Since the mass of the flywheel remains constant, we can ignore it in our calculations.
Change in Moment of Inertia = (1/2) * (Change in Radius)^2
Substituting the value of the change in radius, we get:
Change in Moment of Inertia = (1/2) * (0.005 * Original Radius)^2 = (1/2) * (0.000025) * (Original Radius)^2
Simplifying further, we find:
Change in Moment of Inertia = 0.0000125 * (Original Radius)^2
Answer:
From the above calculation, we can conclude that the percent increase in the moment of inertia about the central axis is 0.00125%, which is equivalent to 0.5% (option 4).
Therefore, the correct answer is option 4) 0.5%.
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During rotation the diameter of a flywheel increases by 1% the percent increases in its moment of inertia about the central axis is 1) 1 %. 2 )% 3 ) % 4)0.5%?
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During rotation the diameter of a flywheel increases by 1% the percent increases in its moment of inertia about the central axis is 1) 1 %. 2 )% 3 ) % 4)0.5%? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about During rotation the diameter of a flywheel increases by 1% the percent increases in its moment of inertia about the central axis is 1) 1 %. 2 )% 3 ) % 4)0.5%? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for During rotation the diameter of a flywheel increases by 1% the percent increases in its moment of inertia about the central axis is 1) 1 %. 2 )% 3 ) % 4)0.5%?.
During rotation the diameter of a flywheel increases by 1% the percent increases in its moment of inertia about the central axis is 1) 1 %. 2 )% 3 ) % 4)0.5%? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about During rotation the diameter of a flywheel increases by 1% the percent increases in its moment of inertia about the central axis is 1) 1 %. 2 )% 3 ) % 4)0.5%? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for During rotation the diameter of a flywheel increases by 1% the percent increases in its moment of inertia about the central axis is 1) 1 %. 2 )% 3 ) % 4)0.5%?.
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