Question

what will be the radius of gyration of a circular plate of diameter 10 cm?​

Answer 1

2.5cm

radious of gyration K=(I/A)^1/2

A =78.53cm^2

therefore k=2.5cm

Answer 2

Given:

• Diameter = 10 cm

To Find:

• The radius of gyration.

Solution:

The formula to find the radius of gyration is given by,

k = √(I/A) → {equation 1}

Where "I" is the moment of inertia, "A" is the area of the circle.

Now we need to find the value of "I" and "A" in order to find the radius of gyration.

1. To find the moment of inertia(I).

The formula to find the moment of inertia of a circle is given by,

I = (π×$D^4$)/64 → {equation 2}

Where "D" is the diameter and "π" has a constant value (3.14)

On substituting the given values we get,

⇒ I = (3.14×$10^4$)/64 = (3.14×10000)/64 {multiplying the terms in numerator}

⇒ I = 31400/64 {dividing the terms}

⇒ I = 490.625 $cm^4$

2. To find the area of the circle(A).

The formula to find the area of the circle is,

A = π×$r^2$ = π×$(d/2)^2$→ {equation 3}

Where "r" is the radius of the circle(r=d/2)

⇒ A = π×$(d/2)^2$

On substituting the values in equation 3 we get,

⇒ A = 3.14×(25) {multiplying the terms}

⇒ A = 78.5 $cm^2$

Now on substituting the values of "I" and "A" in equation 1 we get,

k = √(490.625/78.5) {dividing the terms}

k = √(6.25) {square root of the value}

k = 2.5cm

∴ The radius of gyration = 2.5 cm.