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Conical pendulum: speed or tension

This type of question, asked 2 times: 2021 Paper 19, 24 Jan 2025. All 2 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    2021 Paper 19

    3
    A particle of mass mm is suspended from a ceiling through a string of length LL. The particle moves in a horizontal circle of radius rr such that r=L2r=\frac{L}{\sqrt{2}}. The speed of particle will be:

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  2. Question 2

    24 Jan 2025

    97
    A string of length LL is fixed at one end and carries a mass of M at the other end. The mass makes (3π)\left( \frac{3}{\pi} \right) rotations per second about the vertical axis passing through end of the string as shown. The tension in the string is ______\_\_\_\_\_\_ ML.