Which of the following has the highest moment of inertia...

Name: Problem 71, Chapter 5: Objective Physics : NEET 2020 Examination textbook Gurukul Oswal
Uploaded: 2021-09-30T16:13:39-08:00
Duration: 1 min 3 s
Channel: Narayan Hari
Description: Which of the following has the highest moment of inertia when each of them has the same mass and the same outer radius: (a) a ring about its axis, perpendicular to the plane of the ring. (b) a disc about its axis, perpendicular to the plane of the disc. (c) a solid sphere about one of its diameters. (d) a spherical shell about one of its diameters.

Which of the following has the highest moment of inertia when each of them has the same mass and the same outer radius: (a) a ring about its axis, perpendicular to the plane of the ring. (b) a disc about its axis, perpendicular to the plane of the disc. (c) a solid sphere about one of its diameters. (d) a spherical shell about one of its diameters.

Which of the following has the highest moment of inertia when each of them has the same mass and the same outer radius:
(a) a ring about its axis, perpendicular to the plane of the ring.
(b) a disc about its axis, perpendicular to the plane of the disc.
(c) a solid sphere about one of its diameters.
(d) a spherical shell about one of its diameters.

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Key Concepts

Mass Distribution

The distribution of mass within an object is crucial because mass elements that are farther from the axis of rotation contribute more significantly to the moment of inertia. This concept explains why objects with the same mass and overall size can have different moments of inertia based solely on how their mass is arranged.

Geometric Dependence

Different shapes have derivable standard formulas for moment of inertia when rotated about specific axes. These formulas encapsulate how the geometry of an object influences its rotational properties, highlighting that objects with larger average distances of mass from the axis will have higher moments of inertia.

Moment of Inertia

Moment of inertia is a physical quantity that measures an object's resistance to changes in its rotational motion. It depends on both the total mass of the object and how that mass is distributed relative to the axis of rotation.

Axis of Rotation

The axis about which an object rotates plays a key role in determining its moment of inertia. Even for a given shape, changing the axis can drastically alter the moment of inertia because the relative distances of mass elements to the axis change, thereby affecting the rotational inertia.

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