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A thin uniform circular disc of mass M and radius R is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with an angular velocity `omega.` another disc of the same dimensions but of mass M/4 is placed gently on the first disc coaxially. The angular velocity of the system now is `2 omega //sqrt5.`

Text Solution

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` vectau = (dvecL)/(dt) Since vectau = 0`
`:. vecL = constant`
`:. I_1 omega_1 = I_2omega_2`
`I_1 = (1)/(2) MR^2`
`omega_1 = omega`
`I_2 = (1)/(2) MR^2 + (1)/(2) (M)/(4)R^2 = ((4+1)/(8)) MR^2 = (5)/(8)MR^2`
`omega_2 = ?`
`omega_2 = (I_1omega_1)/(I_2) = +((1)/(2)MR^2xxomega)/(5)/(8)MR^2 = (8)/(2xx5) omega = (4)/(5)omega`
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