A nucleus disintegrates into two nuclear parts which have their velocities in the ratio $2: 1$. The ratio of…

A nucleus disintegrates into two nuclear parts which have their velocities in the ratio $2: 1$. The ratio of their nuclear sizes will be
  1. $2^{1 / 3}: 1$
  2. $1: 3^{1 / 2}$
  3. $3^{1 / 2}: 1$
  4. $1: 2^{1 / 3}$

Solution

$\frac{R_1}{R_2}=\left(\frac{m_2}{2 m_2}\right)^{1 / 3}$ $\Rightarrow \frac{R_1}{R_2}=1: 2^{1 / 3}$

Asked in: JEE Main 2004

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