Two discs are rotating about their normal axes, passing through their centres and perpendicular to plane of the discs. Disc D₁has 2 kg mass and 0.2m radius and initial angular velocity of 50rads^–1. Disc D₂ has 4kg mass and 0.1 m radius and initial angular velocity of 200rads^–1. The two discs are brought in contact face to face, with their axes of rotation coincident. The final angular velocity (in rads^–1) of the system is

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100

120

answer is B.

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Detailed Solution

$I_{1} ω_{1} + I_{2} ω_{2} = (I_{1} + I_{2}) ω$

$\frac{m_{1} {r_{1}}^{2}}{2} ω_{1} + \frac{m_{2} {r_{2}}^{2}}{2} ω_{2} = (\frac{m_{1} {r_{1}}^{2}}{2} + \frac{m_{2} {r_{2}}^{2}}{2}) ω$

$(100 x 0 . 2^{2} x 50 + 4 x 0 . 1^{2} x 200) = = (2 x 0 . 2^{2} + 4 x 0.12) ω$

$\Rightarrow 1200 = 12 ω$

$ω = 100 r a d / s$

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