Ncert Exercises & Solutions

Q. 15 Why does a solid sphere have a smaller moment of inertia than a hollow cylinder of the same mass and radius, about an axis passing through their axes of symmetry?

Hint: Use moment of inertia,

I = {Σm}_{i} r_{i}^{2} .

$I = {Σm}_{i} r_{i}^{2} .$

Step 1: Interpret the answer.

The moment of inertia of a body is given by

I = {Σm}_{i} r_{i}^{2}

$I = {Σm}_{i} r_{i}^{2}$ [sum of moment of inertia of each constituent particles]

All the mass in a cylinder lies at distance R from the axis of symmetry but most of the mass of a solid sphere lies at a smaller distance than R.

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