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The moment of inertia of a circular disc about one of its diameter is I. What will be its moment of inertia about a tangent parallel to the diameter is nI , then find n.
Correct answer is '5'. Can you explain this answer?
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The moment of inertia of a circular disc about one of its diameter is...
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The moment of inertia of a circular disc about one of its diameter is...
Explanation:
The moment of inertia of a circular disc about one of its diameters is given by the formula:
I = (1/4) * MR²
where M is the mass of the disc and R is the radius of the disc.
Moment of Inertia about a Tangent:
To find the moment of inertia about a tangent parallel to the diameter, we can use the parallel axis theorem. According to the parallel axis theorem, the moment of inertia about an axis parallel to and a distance 'd' away from an axis passing through the center of mass is given by:
I' = I + Md²
where I' is the moment of inertia about the new axis, I is the moment of inertia about the center of mass, M is the mass of the object, and d is the perpendicular distance between the two axes.
In this case, the moment of inertia about the center of mass is I, and the distance 'd' between the two axes is R/2 (since the tangent is parallel to the diameter). Substituting these values into the equation, we get:
I' = I + M(R/2)²
Simplifying this equation, we have:
I' = I + (1/4)MR²
Comparing this equation with the formula for the moment of inertia about the diameter, we can see that I' is equal to 5 times I. Therefore, n = 5.
Conclusion:
The moment of inertia of a circular disc about a tangent parallel to the diameter is 5 times the moment of inertia about the diameter.
The moment of inertia of a circular disc about one of its diameters is given by the formula:
I = (1/4) * MR²
where M is the mass of the disc and R is the radius of the disc.
Moment of Inertia about a Tangent:
To find the moment of inertia about a tangent parallel to the diameter, we can use the parallel axis theorem. According to the parallel axis theorem, the moment of inertia about an axis parallel to and a distance 'd' away from an axis passing through the center of mass is given by:
I' = I + Md²
where I' is the moment of inertia about the new axis, I is the moment of inertia about the center of mass, M is the mass of the object, and d is the perpendicular distance between the two axes.
In this case, the moment of inertia about the center of mass is I, and the distance 'd' between the two axes is R/2 (since the tangent is parallel to the diameter). Substituting these values into the equation, we get:
I' = I + M(R/2)²
Simplifying this equation, we have:
I' = I + (1/4)MR²
Comparing this equation with the formula for the moment of inertia about the diameter, we can see that I' is equal to 5 times I. Therefore, n = 5.
Conclusion:
The moment of inertia of a circular disc about a tangent parallel to the diameter is 5 times the moment of inertia about the diameter.
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The moment of inertia of a circular disc about one of its diameter is I. What will be its moment of inertia about a tangent parallel to the diameter is nI , then find n.Correct answer is '5'. Can you explain this answer?
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