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The ratio of moment of inertia of a circular plate to that of a square plate for equal depth is
- a)less than one
- b)equal to one
- c)greater than one
- d)none of the above
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The ratio of moment of inertia of a circular plate to that of a square...
Concept:
Moment of inertia of circular plate,
Moment of inertia of Square plate,
Calculation:
The ratio of the moment of inertia of a circular plate to that of a square plate is, Which is less than 1.
Important Points
The following table shows the Second moment of inertia of different shapes
Moment of inertia of circular plate,
Moment of inertia of Square plate,
Calculation:
The ratio of the moment of inertia of a circular plate to that of a square plate is, Which is less than 1.
Important Points
The following table shows the Second moment of inertia of different shapes
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The ratio of moment of inertia of a circular plate to that of a square...
The moment of inertia is a property of an object that measures its resistance to rotational motion. It depends on the mass distribution of the object and the axis of rotation. For a circular plate and a square plate of equal depth, the mass is distributed differently, leading to different moment of inertia values.
The moment of inertia of a circular plate is given by the formula:
I_circular = (1/4) * m * r^2
where m is the mass of the plate and r is the radius of the plate.
The moment of inertia of a square plate is given by the formula:
I_square = (1/12) * m * h^2
where m is the mass of the plate and h is the side length of the square plate.
To compare the two moment of inertia values, we can take the ratio of I_circular to I_square:
I_circular / I_square = [(1/4) * m * r^2] / [(1/12) * m * h^2]
The mass cancels out in the ratio, so we are left with:
I_circular / I_square = (r^2) / (3 * h^2)
From the equation, we can see that the ratio of the moment of inertia of a circular plate to that of a square plate depends on the ratio of r^2 to h^2.
Now, let's consider a circular plate and a square plate with equal depth. This means that the height of the square plate is equal to the diameter of the circular plate (h = 2r). Substituting this into the ratio equation:
I_circular / I_square = (r^2) / (3 * (2r)^2) = (r^2) / (12r^2) = 1/12
So, the ratio of moment of inertia of a circular plate to that of a square plate for equal depth is 1/12, which is less than one. Therefore, the correct answer is option A: less than one.
The moment of inertia of a circular plate is given by the formula:
I_circular = (1/4) * m * r^2
where m is the mass of the plate and r is the radius of the plate.
The moment of inertia of a square plate is given by the formula:
I_square = (1/12) * m * h^2
where m is the mass of the plate and h is the side length of the square plate.
To compare the two moment of inertia values, we can take the ratio of I_circular to I_square:
I_circular / I_square = [(1/4) * m * r^2] / [(1/12) * m * h^2]
The mass cancels out in the ratio, so we are left with:
I_circular / I_square = (r^2) / (3 * h^2)
From the equation, we can see that the ratio of the moment of inertia of a circular plate to that of a square plate depends on the ratio of r^2 to h^2.
Now, let's consider a circular plate and a square plate with equal depth. This means that the height of the square plate is equal to the diameter of the circular plate (h = 2r). Substituting this into the ratio equation:
I_circular / I_square = (r^2) / (3 * (2r)^2) = (r^2) / (12r^2) = 1/12
So, the ratio of moment of inertia of a circular plate to that of a square plate for equal depth is 1/12, which is less than one. Therefore, the correct answer is option A: less than one.
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The ratio of moment of inertia of a circular plate to that of a square plate for equal depth isa)less than oneb)equal to onec)greater than oned)none of the aboveCorrect answer is option 'A'. Can you explain this answer?
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