JEE Main · 2022 · 26 Jul 2022 · Shift 2 · Rotational Mechanics

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The radius of gyration of a cylindrical rod about an axis of rotation perpendicular to its length and passing through the center will be ______ m.

Given, the length of the rod is

103

Answer: 5

Solution

For a uniform rod of length

ℓ

rotating about an axis perpendicular to its length through the center, the moment of inertia is

I = \frac{m ℓ ^{2}}{12}

. By definition,

I = m k^{2}

, where k is the radius of gyration. Therefore,

k^{2} = \frac{ℓ ^{2}}{12}

, giving

k = \frac{ℓ}{2 3} = \frac{10 3}{2 3} = 5

JEE Main · 2022 · 26 Jul 2022 · Shift 2 · Integer answer

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