Sir what is radius of gyration?

1.	Sir what is radius of gyration?
Answer» The formula of moment inertia in terms of the radius of gyration is given as follows:I\xa0=\xa0mk2 (1)where\xa0I\xa0is the moment of inertia and\xa0m\xa0is the mass of the bodyAccordingly, the radius of gyration is given as followsk=√I/m (2)The unit of radius of gyration is mm. By knowing the radius of gyration, one can find the moment of inertia of any complex body equation (1) without any hassle.Consider a body having\xa0n\xa0number of particles each having a mass of\xa0m. Let the perpendicular distance from the axis of rotation be given by\xa0r1,\xa0r2,\xa0r3,…,rn. We know that the moment of inertia in terms of radius of gyration is given by the equation (1). Substituting the values in the equation, we get the moment of inertia\xa0of the body as follows………… (3)If all the particles have the same mass then equation (3) becomesWe can write mn as M which signifies the total mass of the body. Now the equation becomes………… (4)From equation (4), we getFrom the above equation, we can infer that the radius of gyration can also be defined as the root mean square distance of various particle of the body from the axis of rotation.

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