First slide

Moment of intertia

Question

If two discs have same mass and thickness but their densities are $ρ_{1}$ and $ρ_{2}$ then the ratio of their moments of inertia about central axis will be [BCECE (Mains) 2012]

Moderate

A

1 : $ρ_{1}$ $ρ_{2}$
B

$ρ_{1}$ $ρ_{2}$ : 1
C

$ρ_{1}$ : $ρ_{2}$
D

$ρ_{2}$ : $ρ_{1}$

Solution

Moment of inertia of disc, $I = \frac{1}{2} M R^{2} = \frac{1}{2} M (\frac{M}{π ρ t})$
$(∵ ρ = \frac{M}{V} = \frac{M}{π R^{2} t}, ∴ R^{2} = \frac{M}{π ρ t})$
$I = \frac{1}{2} \frac{M^{2}}{π ρ t}$
$∴ I \propto \frac{1}{ρ}$ (As, M and t are constants)
$∵ \frac{I_{1}}{I_{2}} = \frac{ρ_{2}}{ρ_{1}}$

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