The radius of gyration of a disc of mass 100 g and radius 5 cm about an axis passing through its centre of gravity and perpendicular to the plane is

We consider the moment of inertia of a disc with a mass of 100 grams and a radius of 5 cm about an axis passing through its center of gravity and perpendicular to the plane of the disc. The moment of inertia for a solid disc is a specific property that quantifies how its mass is distributed relative to the rotation axis.

This concept of radius of gyration simplifies the thinking where we could imagine the entire mass of the disc concentrated at a certain distance from the axis of rotation. We can get this distance using the mass and radius of the disc. Then, using principles from rotational motion, we can relate the radius of gyration in terms of mass and radius of the disc.

By using the provided mass and radius values in the calculations, we find that the radius of gyration is approximately 3.54 cm. This value is an effective distance from the rotation axis where the mass can be assumed to be concentrated for the purposes of rotational dynamics. The radius of gyration is an important parameter in engineering and physics as it helps predict the behavior of rotating objects.

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