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Conical pendulum: tension in the string or angular velocity

The same question, asked 3 times: 11 May 2024 S1*, 14 May 2024 S1*, 13 Apr 2026 S1. Every wording below, oldest first.

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  1. Question 1

    11 May 2024 S1

    12
    A ball of mass mm is attached to the free end of a string of length ll. The ball is moving in horizontal circular path about the vertical axis as shown in the diagram. The angular velocity ω\omega of the ball will be [TT = Tension in the string.]

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  2. Question 2

    14 May 2024 S1

    44
    A string of length 'LL' fixed at one end carries a body of mass 'm' at the other end. The mass is revolved in a circle in the horizontal plane about a vertical axis passing through the fixed end of the string. The string makes angle 'θ\theta' with the vertical. The angular frequency of the body is 'ω\omega'. The tension in the string is

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  3. Question 3

    13 Apr 2026 S1

    104
    A string of length 'L' fixed at one end carries a mass 'm' at the other end. The string makes 3π\dfrac{3}{\pi} r.p.s. around the vertical axis through fixed end. The tension in the string is

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