One solid sphere A and another hollow sphere B are of same mass and same outer radii. Their moment of inertia about their diameters are respectively $\mathrm{I}_{\mathrm{A}}$ and $\mathrm{I}_{\mathrm{B}}$ such that Where $\mathrm{d}_{\mathrm{A}}$ and $\mathrm{d}_{\mathrm{B}}$ are their densities.

(B) $\mathrm{I}_{\mathrm{A}}>\mathrm{I}_{\mathrm{B}}$

(D) $\mathrm{I}_{\mathrm{A}} / \mathrm{I}_{\mathrm{B}}=\mathrm{d}_{\mathrm{A}} / \mathrm{d}_{\mathrm{B}}$

JEE Main · 2004 · 24 Apr 2004 · Offline · Rotational Mechanics

One solid sphere A and another hollow sphere B are of same mass and same outer radii. Their moment of inertia about their diameters are respectively

I_{A}

and

I_{B}

such that

Where

d_{A}

and

d_{B}

are their densities.

(A) $I_{A} = I_{B}$
(B) $I_{A} > I_{B}$
(C) $I_{A} < I_{B}$ ✓ Correct
(D) $I_{A} / I_{B} = d_{A} / d_{B}$

Answer: (C)

Solution

About a diameter the solid sphere has moment of inertia

\frac{2}{5} M R^{2}

, while the hollow sphere has

\frac{2}{3} M R^{2}

. For the same mass and radius,

\frac{2}{5} M R^{2} < \frac{2}{3} M R^{2}

, so the solid sphere has the smaller moment of inertia; the hollow sphere, with its mass carried out at the surface, has the larger one.

JEE Main · 2004 · 24 Apr 2004 · Offline · Single correct option

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