If the length of a thin uniform rod is L and | vedclass

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(A) The moment of inertia $I$ of a thin uniform rod of mass $M$ and length $L$ about an axis perpendicular to its length and passing through one end i

Vedclass · Accepted Answer

$1: \sqrt{3}$

Vedclass · Answer

(A) The moment of inertia $I$ of a thin uniform rod of mass $M$ and length $L$ about an axis perpendicular to its length and passing through one end is given by $I = \frac{1}{3}ML^2$.By definition, the radius of gyration $K$ is related to the moment of inertia by $I = MK^2$.Equating the two expressions for $I$, we get $MK^2 = \frac{1}{3}ML^2$.Canceling $M$ from both sides, we have $K^2 = \frac{L^2}{3}$.Taking the square root of both sides, we get $K = \frac{L}{\sqrt{3}}$.Therefore, the ratio $K: L = \frac{1}{\sqrt{3}}$ or $1: \sqrt{3}$.

If the length of a thin uniform rod is $L$ and the radius of gyration of the rod about an axis perpendicular to its length and passing through one end is $K$, then $K: L=$

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