A round disc of moment of inertia I₂, about its axis perpendicular to its plane and passing through its centre is placed over another disc of moment of inertia I₁, rotating with an angular velocity $ω$ about the same axis. The final angular velocity of the combination of discs is

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$\frac{I_{2} ω}{I_{1} + I_{2}}$

$ω$

$\frac{I_{1} ω}{I_{1} + I_{2}}$

$\frac{(I_{1} + I_{2}) ω}{I_{1}}$

answer is C.

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Detailed Solution

Applying the law of conservation of angular momentum, we get,
$\begin{aligned} I_{1} ω_{1} = (I_{1} + I_{2}) ω_{2} \\ or I_{1} ω = (I_{1} + I_{2}) ω_{2} \\ ∴ ω_{2} = (\frac{I_{1} ω}{I_{1} + I_{2}}) \end{aligned}$

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