First slide

Moment of intertia

Question

One solid sphere A and another hollow sphere B are of same mass and same outer radius. Their moments
of inertia about their diameters are respectively, I_A and I_B such that

Easy

A

$I_{A} = I_{B}$
B

$I_{A} > I_{B}$
C

$I_{A} < I_{B}$
D

None of these

Solution

Let same mass and same outer radii of solid sphere and hollow sphere be M and R, respectively. The moment of inertia of solid sphere A about its diameter,
$I_{A} = \frac{2}{5} M R^{2}$ …(i)
The moment of inertia of hollow sphere (spherical shell) B
about its diameter, $I_{B} = \frac{2}{3} M R^{2}$ …(ii)
From Eqs. (i) and (ii), we get
$I_{A} < I_{B}$

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