本题目来源于试卷: 2007美国US F=MA物理竞赛，类别为 美国F=MA物理竞赛
[单选题]
A thin, uniform rod 5acu5yyy*2s152,f n iujp/e pl n4rgdrf w- 1nm1l.xbs 2k*a*gahdg.has mass $m$ and length $L$. Let the acceleration due to gravity be $g$. Let the rotational inertia of the rod about its center be $md^{2}$. Find the ratio $L/d$.
A. $3\sqrt{2}$
B. $3$
C. $12$
D. $2\sqrt{3}$
E. none of the above
参考答案: D
本题详细解析:
The rotational inertia of a thin,(,zqe *m aarn9xud3f, uniform rod about its center ($I_{cm}$) is given by the formula $I_{cm} = \frac{1}{12}mL^2$.
The problem states that $I_{cm} = md^2$.
By equating these two expressions, we get:
$md^2 = \frac{1}{12}mL^2$
$d^2 = \frac{L^2}{12}$
$\frac{L^2}{d^2} = 12$
Taking the square root of both sides gives:
$\frac{L}{d} = \sqrt{12} = \sqrt{4 \times 3} = 2\sqrt{3}$.
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