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Q18 (NDA-II/2019) Science & Technology › Basic Science (Physics, Chemistry, Biology) › Basic mechanics concepts

A solid disc and a solid sphere have the same mass and same radius. Which one has a higher moment of inertia about its centre of mass?

Result
Your answer: —  ·  Correct: A
Explanation

The moment of inertia (I) of an object depends on its mass distribution relative to the axis of rotation. For a solid disc of mass M and radius R, the moment of inertia about its center of mass (perpendicular to its plane) is given by the formula I = (1/2)MR², which equals 0.5MR². In contrast, the moment of inertia for a solid sphere of the same mass and radius is I = (2/5)MR², which equals 0.4MR². Comparing these values, 0.5MR² is greater than 0.4MR². This difference arises because the mass in a solid sphere is distributed more towards the center in three dimensions, whereas in a disc, more mass is concentrated further from the axis. Therefore, the solid disc has a higher moment of inertia than the solid sphere when both have identical mass and radius.

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