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Moment of Inertia of Hollow Sphere

I1 and I2 a...

Question

$I_{1}$ and $I_{2}$ are moments of inertia of two solid spheres of same mass about the axes passing through their centres. If first sphere is made of wood and the second is made of steel, then

A

I_{1} = I_{2}

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B

I_{1} < I_{2}

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C

I_{1} > I_{2}

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D

I_{1} \leq I_{2}

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Solution

The correct option is B $I_{1} > I_{2}$
$I_{s} = \frac{2}{5} m R^{2}$

$m_{1} = m_{2} = m$
$d_{1} < d_{2}$

$d = \frac{m}{v}$

$\frac{m}{V_{1}} < \frac{m}{V_{2}}$
or
$V_{2} < V_{1}$
or
$R_{2} < R_{1}$
Thus we get
$I_{1} > I_{2}$

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