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JEE Main 2018 (15 Apr, Shift 2) · Nucleus: Composition, Size & Nuclear Force

Nucleus: Composition, Size & Nuclear Force question from JEE Main 2018 (15 Apr, Shift 2)

Q26JEE Main 2018 · 15 APR · SHIFT 2Medium

Nucleus: Composition, Size & Nuclear Force

An unstable heavy nucleus at rest breaks into two nuclei which move away with velocities in the ratio of 8: 27. The ratio of the radii of the nuclei (assumed to be spherical) is:

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Answer: (c)

  1. Parent at rest, so momentum is conserved: m1v1=m2v2⇒A1A2=v2v1=278m_1v_1 = m_2v_2 \Rightarrow \dfrac{A_1}{A_2} = \dfrac{v_2}{v_1} = \dfrac{27}{8}
  2. R∝A1/3⇒R1R2=(278)1/3=32R \propto A^{1/3} \Rightarrow \dfrac{R_1}{R_2} = \left(\dfrac{27}{8}\right)^{1/3} = \dfrac{3}{2}
  3. So the answer is (c) 3:23:2.
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