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Vertical circle: speed, change in velocity or kinetic energy at a point

This type of question, asked 4 times: 2021 Paper 14, 27 Jun 2022, 29 Jan 2025, 24 Jan 2026 S2. All 4 questions below, oldest first.

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  1. Question 1

    2021 Paper 14

    6
    A particle tied to string of length 0.5 m0.5\text{ }m is given a velocity 3 ms−13{\text{ }ms}^{- 1} at its bottom point while undergoing vertical circular motion. What will be its speed when it makes an angle of 60∘60^{\circ} with the lower vertical?

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  2. Question 2

    27 Jun 2022

    95
    A stone tied to a string of length LL is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed uu. The magnitude of change in its velocity, as it reaches a position where the string is horizontal, is x(u2−gL)\sqrt{x\left( u^{2}- gL \right)}. The value of xx is

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  3. Question 3

    29 Jan 2025

    16
    A body of mass ' m ' connected to a massless and unstretchable string goes in a vertical circle of radius ' R ' under gravity g . The other end of the string is fixed at the center of circle. If velocity at top of circular path is ngRn\sqrt{gR}, where, n≥1n \geq 1, then ratio of kinetic energy of the body at bottom to that at top of the circle is

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  4. Question 4

    24 Jan 2026 S2

    5
    In case of vertical circular motion of a particle by a thread of length r if the tension in the thread is zero at an angle 30∘30^{\circ} shown in figure, the velocity at the bottom point (A) of the circular path is (g = gravitational acceleration)

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