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The moment of inertia of a thin uniform rod of mass M and length L about an axis passing through its midpoint and perpendicular to its length is I0. Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is [2011]
- a)I0 + ML2/2
- b)I0 + ML2/4
- c)I0 + 2ML2
- d)I0 + ML2
Correct answer is option 'B'. Can you explain this answer?
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The moment of inertia of a thin uniform rod of mass M and length L abo...
By theorem of parallel axes,
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The moment of inertia of a thin uniform rod of mass M and length L abo...
To solve this problem, we can use the parallel axis theorem, which states that the moment of inertia of a body about any axis parallel to an axis passing through its center of mass is equal to the moment of inertia about the center of mass plus the product of the mass and the square of the distance between the two axes.
Let's consider the moment of inertia of the thin uniform rod about an axis passing through its midpoint and perpendicular to its length. We are given that this moment of inertia is I0.
Now, we need to find the moment of inertia of the rod about an axis passing through one of its ends and perpendicular to its length. Let's call this moment of inertia I1.
We know that the distance between the midpoint of the rod and one of its ends is L/2. Therefore, using the parallel axis theorem, we can write:
I1 = I0 + M * (L/2)^2
Simplifying this equation, we get:
I1 = I0 + M * (L^2/4)
Now, we need to compare this expression with the given options:
a) I0 * (ML^2/2)
b) I0 * (ML^2/4)
c) I0 * 2ML^2
d) I0 * ML^2
Comparing the expression for I1 with the options, we can see that option b) matches our result:
I1 = I0 + M * (L^2/4) = I0 * (ML^2/4)
Therefore, the correct answer is option b) I0 * (ML^2/4).
Let's consider the moment of inertia of the thin uniform rod about an axis passing through its midpoint and perpendicular to its length. We are given that this moment of inertia is I0.
Now, we need to find the moment of inertia of the rod about an axis passing through one of its ends and perpendicular to its length. Let's call this moment of inertia I1.
We know that the distance between the midpoint of the rod and one of its ends is L/2. Therefore, using the parallel axis theorem, we can write:
I1 = I0 + M * (L/2)^2
Simplifying this equation, we get:
I1 = I0 + M * (L^2/4)
Now, we need to compare this expression with the given options:
a) I0 * (ML^2/2)
b) I0 * (ML^2/4)
c) I0 * 2ML^2
d) I0 * ML^2
Comparing the expression for I1 with the options, we can see that option b) matches our result:
I1 = I0 + M * (L^2/4) = I0 * (ML^2/4)
Therefore, the correct answer is option b) I0 * (ML^2/4).
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The moment of inertia of a thin uniform rod of mass M and length L about an axis passing through its midpoint and perpendicular to its length is I0. Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is [2011]a)I0 + ML2/2b)I0 + ML2/4c)I0 + 2ML2d)I0 + ML2Correct answer is option 'B'. Can you explain this answer?
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