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A circular disc is rotating about its natural axis with angular velocity of 10 rads^–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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2.5 rads^–1

5 rads^–1

8 rads^–1

6 rads^–1

answer is C.

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Detailed Solution

$I_{1} = \frac{{MR}^{2}}{2}, I_{2} = \frac{M}{2} {(\frac{R}{2})}^{2} = \frac{{MR}^{2}}{8}$

$ω_{1} = 10, ω_{2} = 0, ω = ?$

Since the angular momentum is conserved in the absence of an external force,

$(I_{1} + I_{2}) ω = I_{1} ω_{1} + I_{2} ω_{2}$
$\Rightarrow ω = \frac{I_{1} ω_{1} + I_{2} ω_{2}}{I_{1} + I_{2}} = \frac{\frac{{MR}^{2}}{2} (10) + \frac{{MR}^{2}}{8} (0)}{\frac{{MR}^{2}}{2} + \frac{{MR}^{2}}{8}}$

$\Rightarrow ω = \frac{\frac{{MR}^{2}}{2} (10)}{\frac{5 {MR}^{2}}{8}} = \frac{10 x 8}{10} = 8 rad / s$

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