A circular disc is rotating about its natural axis with angular velocity of 110rads^-1. A second disc of same mass is joined to it coaxially. If the radius of disc is half of the radius of the first, then they together rotate with an angular velocity of

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8 rad s^-1

5 rad s^-1

6 rad s^-1

2.5 rad s^-1

answer is C.

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Detailed Solution

In this case the total angular momentum is conserved.

$I_{1} = \frac{{MR}^{2}}{2} and I_{2} = \frac{M}{2} {[\frac{R}{2}]}^{2}$

$\frac{{MR}^{2}}{2} \times 10 = [\frac{{MR}^{2}}{2} + \frac{{MR}^{2}}{8}] \times ω$

$\Rightarrow ω = 8 rad / s$

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