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Nucleus breaks into two parts: ratio of their sizes from the ratio of their speeds, or the reverse

The same question, asked 2 times: 25 Jan 2023*, 11 Apr 2023. Every wording below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    25 Jan 2023

    113
    A nucleus disintegrates into two smaller parts, which have their velocities in the ratio 3:23:2. The ratio of their nuclear sizes will be (x3)13\left( \frac{x}{3} \right)^{\frac{1}{3}}. The value of ' xx ' is: -

  2. Question 2

    11 Apr 2023

    113
    A nucleus disintegrates into two nuclear parts, in such a way that ratio of their nuclear sizes is 1:21/31:2^{1/3}. Their respective speed have a ratio of n:1n:1. The value of nn is___