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JIPMER 2015
Exam
JIPMER
Year
2015
Subject
Physics
Chapter
Nuclear Physics

JIPMER 2015 · Physics · Nuclear Physics

A nucleus disintegrates into two nuclear parts which have their...

A nucleus disintegrates into two nuclear parts which have their velocities in the ratio 2:12: 1. The ratio of their nuclear size will be

Options

  1. A21/3:12^{1 / 3}: 1
  2. B1:31/21: 3^{1 / 2}
  3. C31/2:13^{1 / 2}: 1
  4. D1:21/31: 2^{1 / 3}

Correct answer

D. 1:21/31: 2^{1 / 3}

Step-by-step solution

According to the law of conservation of momentum, we get m1V1=m2V2m_1 V_1=m_2 V_2 or (m1m2)=\left(\frac{m_1}{m_2}\right)=\left(\frac{v_2}{v_1}\right)ButButm=\frac{4}{3} \pi r^3 \rho \text{ or } m \propto r^3 ⇒m1m2=r13r23∴r13r23=V2V1=12⇒r1r2=(12)1/3∴r1:r2=1:(2)1/3\begin{array}{ll}\Rightarrow & \frac{m_1}{m_2}=\frac{r_1^3}{r_2^3} \\ \therefore & \frac{r_1^3}{r_2^3}=\frac{V_2}{V_1}=\frac{1}{2} \\ \Rightarrow & \frac{r_1}{r_2}=\left(\frac{1}{2}\right)^{1 / 3} \\ \therefore & r_1: r_2=1:(2)^{1 / 3}\end{array}
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