Question

The radius of guration of a uniform rod of length L about an axis passing through its centre of mass and perpendicular to its length is,

Answer 1

Answer:

The radius of gyration of a uniform rod of length L about an axis passing through its center of mass and perpendicular to its length is 0.29 L

Explanation:

As we know that moment of inertia of the rod about an axis passing through its center of mass and perpendicular to the rod is given as

$I = \frac{1}{12}mL^2$

now radius of gyration is the equivalent distance of the point mass from the axis at which its moment of inertia is same as that of rigid body

so here we have

$I = \frac{1}{12}mL^2$

$mk^2 = \frac{1}{12} mL^2$

$k = \frac{L}{\sqrt{12}}$

$k = 0.29 L$

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Topic : Radius of gyration

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