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Which of the following equation represents Moment of Inertia of a plane region relative to x-axis?
- a)∬y2 f(x, y)dxdy
- b)∬x2 f(x, y)dxdy
- c)∬xf(x, y)dxdy
- d)∬yf(x, y)dxdy
Correct answer is option 'A'. Can you explain this answer?
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Which of the following equation represents Moment of Inertia of a plan...
Moment of Inertia of a plane region,
Relative to x-axis is given by,
Ixx =∬y2 f(x, y)dxdy
Relative to y-axis is given by,
Iyy =∬x2 f(x, y)dxdy
Relative to x-axis is given by,
Ixx =∬y2 f(x, y)dxdy
Relative to y-axis is given by,
Iyy =∬x2 f(x, y)dxdy
Most Upvoted Answer
Which of the following equation represents Moment of Inertia of a plan...
Moment of Inertia of a plane region,
Relative to x-axis is given by,
Ixx =∬y2 f(x, y)dxdy
Relative to y-axis is given by,
Iyy =∬x2 f(x, y)dxdy
Relative to x-axis is given by,
Ixx =∬y2 f(x, y)dxdy
Relative to y-axis is given by,
Iyy =∬x2 f(x, y)dxdy
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Which of the following equation represents Moment of Inertia of a plan...
Explanation:
Moment of Inertia of a plane region relative to x-axis:
The moment of inertia of a plane region relative to the x-axis is given by the integral of y^2 f(x, y)dA, where f(x, y) represents the density function of the region and dA represents the differential area element.
Explanation of the equation:
- The equation y^2 f(x, y)dxdy represents the moment of inertia of a plane region relative to the x-axis.
- Here, y^2 represents the distance of an element of area from the x-axis squared, which is a key component in calculating the moment of inertia.
- The integral is taken over the region of interest, with f(x, y) representing the density function of the region.
- The integral is taken with respect to both x and y, as we are calculating the moment of inertia relative to the x-axis.
Therefore, the correct equation representing the moment of inertia of a plane region relative to the x-axis is y^2 f(x, y)dxdy (option A).
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Which of the following equation represents Moment of Inertia of a plane region relative to x-axis?a)y2 f(x, y)dxdyb)x2 f(x, y)dxdyc)xf(x, y)dxdyd)yf(x, y)dxdyCorrect answer is option 'A'. Can you explain this answer?
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