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A cubical block has mass 4 kg. The radius of gyration of the block about an axis is 2 m. find the moment of inertia of the block about the axis for which the radius of gyration is given.

A cubical block has mass 4 kg. The radius of gyration of the block about an axis is 2 m. find the moment of inertia of the block about the axis for which the radius of gyration is given. Correct Answer 16 kg m<sup>2</sup>

Concept:

  • Moment of inertia: The property of a rigid body that opposes the rotational motion is called the moment of inertia. It is denoted by I.
  • The distance from the axis of rotation to a point where the total mass of the body is assumed to be concentrated is called the radius of gyration. It is denoted by k or r.


The moment of inertia about an axis is given by:

I = M k2 where M is the mass of the rigid body and k is the radius of gyration

Calculation:

Given:

mass of the block (M) = 4 kg

Radius of gyration (k) = 2 m

Moment of inertia (I) = M k2 = 4 × 22 = 16 kg m2

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