Question

Moment of inertia of a sphere about its diameter is 2/5 MR2. What is its radius of

gyration about the axis?
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Answer 1

Explanation:

By parallel axis theorem, the moment of inertia at 2R is

I = (2MR2/5) + M(2R)2

I = 22MR2/5

The radius of gyration is

Mk2 = 22MR2/5

Therefore k = √(22/5) ✕ R

Answer 2

The radius of gyration is $\sqrt{ \frac{2}{5} } r$

Given:

The moment of inertia of a sphere about its diameter is 2/5 MR².

To Find:

The radius of gyration about the axis.

Solution:

To find the radius of gyration about the axis, we will follow the following steps:

As we know,

The moment of inertia of a sphere about the axis =

$\frac{2}{5} M {r}^{2}$

Here, r is the radius of the sphere.

Now,

$\frac{2}{5} M {r}^{2} = M {k}^{2}$

Here, k is the radius of gyration.

Also,

In putting values we get,

$\frac{2}{5} {r}^{2} = {k}^{2}$

$k = \sqrt{\frac{2}{5} } r$

Henceforth, the radius of gyration is $\sqrt{ \frac{2}{5} } r$

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