Question

radius of gyration of a uniform disc of radius r about any diameter of a disc is​

Answer 1

• Radius of gyration of a uniform circular disc of radius r about any diameter of a disc is r/2.

Given-

• Disc is uniform so mass distribution will be same about all axis.

We know that moment of inertia is the function of mass and radius. So we can say that

I = f (m, r) = mk² where k is the radius of gyration.

By applying the perpendicular axis theorem-

We know that moment of inertia about a disc is mr²/2

From the attached figure-

I₁ + I₂ = mr²/2

And uniform disc is there so I₁ = I₂

2 I₂ = mr²/2

I₂ = mr²/4

By comparing this equation -

K² = r²/4

So, K = r/2

Answer 2

The radius of gyration about any diameter of a disc is $\dfrac{r}{2}$

Explanation:

Given that,

Radius of disc= r

We know that the radius of gyration

$K=\sqrt{\dfrac{I}{m}}$

$I=mK^2$

Where, K = radius of gyration

We need to calculate the radius of gyration about any diameter of a disc

The moment of inertia of the disc for parallel and perpendicular axis

$I_{1}+I_{2}=\dfrac{mr^2}{2}$

Here, $I_{1}=I_{2}$

$2I_{2}=\dfrac{mr^2}{2}$

$I_{2}=\dfrac{mr^2}{4}$

$mK^2=\dfrac{mr^2}{4}$

$K=\dfrac{r}{2}$

Hence, The radius of gyration about any diameter of a disc is $\dfrac{r}{2}$

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Topic :

https://brainly.in/question/4585382