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Change in angular velocity or kinetic energy when the moment of inertia changes

This type of question, asked 4 times: 26 Apr 2025 S2, 15 Apr 2026 S1, 18 Apr 2026 S2, 14 May 2026 S2. All 4 questions below, oldest first.

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  1. Question 1

    26 Apr 2025 S2

    49
    A man standing on a turntable is rotating at a certain angular frequency with his arms outstretched. He suddenly folds his arms. If his moment of inertia with folded arms is 75%75\% of that with outstretched arms, then his rotational kinetic energy will

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  2. Question 2

    15 Apr 2026 S1

    107
    If the earth suddenly contracts to (13)rd\left(\dfrac{1}{3}\right)^{rd} of its present size without change in its mass, the ratio kinetic energy of the earth after and before contraction will be (Earth is assumed to be a rotating sphere about itself)

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  3. Question 3

    18 Apr 2026 S2

    106
    A kathak dancer is standing on horizontal surface with folded hands. In the begining dancer is rotating about his central axis and his kinetic energy is 'K' at that time. The kathak dancer now stretches his arms so that the moment of inertia of the dancer becomes three times and the angular velocity becomes one-third. The kinetic energy of the dancer now is

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  4. Question 4

    14 May 2026 S2

    106
    A solid sphere is rotating about a diameter at an angular velocity ω\omega. If it cools so that its radius reduces to (1n)th\left(\dfrac{1}{n}\right)^{th} of its original value, its angular velocity becomes

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