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JEE Main 2023 (25 Jan, Shift 2) · Nucleus: Composition, Size & Nuclear Force

Nucleus: Composition, Size & Nuclear Force question from JEE Main 2023 (25 Jan, Shift 2)

Q15JEE Main 2023 · 25 JAN · SHIFT 2Medium

Nucleus: Composition, Size & Nuclear Force

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

Numerical answer type. Work it out, then open the answer.

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Answer: 2

  1. Momentum conservation: A1A2=v2v1=23\dfrac{A_1}{A_2} = \dfrac{v_2}{v_1} = \dfrac{2}{3}
  2. R1R2=(A1A2)1/3=(23)1/3\dfrac{R_1}{R_2} = \left(\dfrac{A_1}{A_2}\right)^{1/3} = \left(\dfrac{2}{3}\right)^{1/3}
  3. Comparing with (x3)1/3\left(\dfrac{x}{3}\right)^{1/3}: x=2x = 2
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