Two discs have same mass and thickness- Their materials are of densities -1 and -2- The rato of their moment of interia about central axis will be

The correct option is D ρ_2 : ρ_1 Moment of inertia of disc I = 12 MR^2 = 12 M (Mπρ t ) ∴ I = 12M^2πρ t ( As ρ = MassVolume = Mπ R^2 t, ther ...

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Standard XII

Physics

Moment of Inertia of a Rod

Two discs hav...

Question

Two discs have same mass and thickness. Their materials are of densities $ρ_{1}$ and $ρ_{2} .$ The rato of their moment of interia about central axis will be

ρ_{1} : ρ_{2}

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ρ_{1} ρ_{2} : 1

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1 : ρ_{1} ρ_{2}

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ρ_{2} : ρ_{1}

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Solution

The correct option is D $ρ_{2} : ρ_{1}$
Moment of inertia of disc
$I = \frac{1}{2} M R^{2} = \frac{1}{2} M (\frac{M}{π ρ t})$
$∴ I = \frac{1}{2} \frac{M^{2}}{π ρ t}$
$(A s ρ = \frac{M a s s}{V o l u m e} = \frac{M}{π R^{2} t}, t h e r e f o r e, R^{2} = \frac{M}{π ρ t})$
$∴ I \propto \frac{1}{ρ}$ (If M and t are constants)
$\Rightarrow \frac{I_{1}}{I_{2}} = \frac{ρ_{2}}{ρ_{1}}$

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Two discs have same mass and thickness. Their materials are of densities ρ1 and ρ2. The rato of their moment of interia about central axis will be

The correct option is D ρ2:ρ1Moment of inertia of discI=12MR2=12M(Mπρt)∴I=12M2πρt(Asρ=MassVolume=MπR2t,therefore,R2=Mπρt)∴I∝1ρ (If M and t are constants)⇒I1I2=ρ2ρ1

Two discs have same mass and thickness. Their materials are of densities $ρ_{1}$ and $ρ_{2} .$ The rato of their moment of interia about central axis will be