Question

Radius of gyration of a solid disc of mass 10 kg about an axis is 0.40 the mi of the disc

Answer 1

answer is 1.6 kg m square....

Answer 2

Answer:

The moment of inertia and radius of gyration about diameter are 0.9 kg-m² and 0.3.

Explanation:

Given that,

Mass of solid = 10 kg

Radius = 0.40 m

Suppose, find the radius of gyration about its diameter and hence calculate moment of inertia about its diameter

We need to calculate the moment of inertia

Using formula of radius of gyration

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

$K=\sqrt{\dfrac{\dfrac{1}{2}MR^2}{M}}$

$K=\sqrt{\dfrac{R^2}{2}}$

Put the value into the formula

$(0.40)^2=\dfrac{R^2}{2}$

$R=\sqrt{2\times(0.40)^2}$

$R=0.6\ m$

We need to calculate the moment inertia of the disc about diameter

Using formula of moment of inertia

$I'=\dfrac{1}{4}MR^2$

Put the value into the formula

$I'=\dfrac{1}{4}\times10\times(0.6)^2$

$I'=0.9\ Kg-m^2$

We need to calculate the radius of gyration about its diameter

Using formula of radius of gyration

$K'=\sqrt{\dfrac{I'}{M}}$

$K'=\sqrt{\dfrac{0.9}{10}}$

$K'=0.3$

Hence, The moment of inertia and radius of gyration about diameter are 0.9 kg-m² and 0.3.