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Chapter 1: Q12DQ (page 294)

A cylindrical body has mass M and radius R. Can the mass be distributed within the body in such a way that its moment of inertia about its axis of symmetry is greater thanMR2? Explain.

Short Answer

Expert verified

No, it is not possible that the moment of inertia about its axis of symmetry will be greater thanMR2.

Step by step solution

01

Concept/Significance of Moment of inertia

The moment of inertia is obtained by multiplying the mass of each particle by the square of its distance from the axis of rotation and by adding these products of the body to this rotation axis.

02

Explain whether the mass is distributed within the body in such a way that its moment of inertia about its axis of symmetry is greater than MR2

No, it is impossible that a cylinder of mass M and radius R have a moment of inertia greater than MR2.

This is because if all the mass are distributed on the shell of the cylinder, then the moment of inertia of the cylinder about its axis of symmetry will beMR2. Since no mass can be placed outside of the shell of the cylinder, then it cannot be greater thanMR2.

Therefore, the moment of inertia about its axis of symmetry will not be greater thanMR2.

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