First slide

Moment of intertia

Question

Two discs have same mass and thickness. Their materials are made of densities d₁ and d₂. The ratio of their moments of inertia about an axis passing through the centre and perpendicular to the plane is

Moderate

A

$d_{1} : d_{2}$
B

$d_{2} : d_{1}$
C

${(\frac{d_{1}}{d_{2}})}^{2}$
D

${(\frac{d_{2}}{d_{1}})}^{2}$

Solution

We have, $(π R^{2} t d) = m$ $(∵ Mass = Density \times Volume)$
$∴ R^{2} = \frac{m}{π t d}$
Now, $I = \frac{1}{2} m R^{2} = \frac{m^{2}}{2 π t d}$
or $I \propto \frac{1}{d}$
$∴$ The ratio of moments of inertia, $\frac{I_{1}}{I_{2}} = \frac{d_{2}}{d_{1}}$

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