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Tension in a string whirled in a vertical circle

This type of question, asked 2 times: May 2021 S1, 2 May 2023 S2. All 2 questions below, oldest first.

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  1. Question 1

    May 2021 S1

    5
    A 1 kg mass is tied to a light inextensible string of length l=103 ml = \frac{10}{3}\ \text{m} and whirled in a vertical circle. The ratio of maximum to minimum tension in the string is 4. The speed of the stone at the highest point of the circle is

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  2. Question 2

    2 May 2023 S2

    50
    The string of a pendulum of length 'L' is displaced through 90∘90^\circ from the vertical and released. Then the maximum strength of the string in order to withstand the tension, as the pendulum passes through the mean position is (m=m = mass of pendulum, g=g = acceleration due to gravity)

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