Q120 / 125 · BITSAT 2020 · Physics

A nucleus splits into two nuclear parts which have their velocity ratio equal to $2: 1 .$ What will be the ratio of their nuclear radius?

  • A
    $2^{1 / 3}: 1$
  • Correct answer
    B
    $1: 2^{1 / 3}$
  • C
    $3^{1 / 2}: 1$
  • D
    $1: 3^{1 / 2}$

Solution

As momentum is conserved, therefore $\frac{\mathrm{m}_{1}}{\mathrm{~m}_{2}}=\frac{\mathrm{A}_{1}}{\mathrm{~A}_{2}}=\frac{\mathrm{v}_{2}}{\mathrm{v}_{1}}=\frac{1}{2}$ $\therefore \frac{\mathrm{R}_{1}}{\mathrm{R}_{2}}=\left(\frac{\mathrm{A}_{1}}{\mathrm{~A}_{2}}\right)^{1 / 3}=\left(\frac{1}{2}\right)^{1 / 3}=1: 2^{1 / 3}$

Hence, the correct answer is option: 'B'.

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