A uniform brass disc of radius and mass m is set into spinning with angular speed $ω_{0}$ , about are axis passing through centre of disc and perpendicular to the plane of disc. If its temperature increases from ${θ_{1}}^{\circ} C to {θ_{2}}^{\circ} C$ without disturbing the disc, what will be its new angular speed ? (the coefficient of linear expansion of brass is $α$ )

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$ω_{0} [1 + 2 α (θ_{2} - θ_{1})]$

$ω_{0} [1 + α (θ_{2} - θ_{1})]$

$\frac{ω_{0}}{[1 + 2 α (θ_{2} - θ_{1})]}$

none of these

answer is C.

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Detailed Solution

Using the principle of conservation of angular momentum, we have
$L_{i} = L_{f} or I_{0} ω_{0} = Iω$
$∴ ω = \frac{I_{0} ω_{0}}{I}$
Here $I = I_{0} [1 + 2 α (θ_{2} - θ_{1})]$
$∴ ω = \frac{I_{0} ω_{0}}{I_{0} [1 + 2 α (θ_{2} - θ_{1})]} = \frac{ω_{0}}{[1 + 2 α (θ_{2} - θ_{1})]}$