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A second disc placed gently on a rotating disc: the new angular velocity

The same question, asked 2 times: 4 May 2023 S2*, 12 May 2024 S1. Every wording below, oldest first.

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  1. Question 1

    4 May 2023 S2

    14
    A thin uniform circular disc of mass 'M' and radius 'R' is rotating with angular velocity 'ω\omega' in a horizontal plane about an axis passing through its centre and perpendicular to its plane. Another disc of same radius but of mass M3\frac{M}{3} is placed gently on the first disc co-axially. The new angular velocity will be

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  2. Question 2

    12 May 2024 S1

    34
    A thin uniform circular disc of mass MM and radius RR is rotating with angular velocity ω\omega in a horizontal plane about an axis passing through its centre and perpendicular to its plane. Another disc of same radius but of mass M2\frac{M}{2} is placed gently on the first disc co-axially. The new angular velocity will be

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