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Mass on a spring whirled in a horizontal circle: extension as a fraction of natural length

The same question, asked 2 times: 10 May 2024 S1*, 22 Apr 2025 S1. Every wording below, oldest first.

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  1. Question 1

    10 May 2024 S1

    46
    A body of mass 200 gram is tied to a spring of spring constant [125] N/m[125]\,\text{N/m}, while the other end of the spring is fixed at point O. If the body moves about O in a circular path on a smooth horizontal surface with constant angular speed 5 rad/s, then the ratio of extension in the spring to its natural length will be

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  2. Question 2

    22 Apr 2025 S1

    19
    A body of mass 100 gram is tied to a spring of spring constant 8 N/m8\text{ }N/m, while the other end of a spring is fixed. If the body moves in a circular path on smooth horizontal surface with constant angular speed 8rad/s8rad/s then the ratio of extension in the spring to its natural length will be

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