Q 12-13-070JEE MainJEE Main 2023 (25 Jan, Shift 2)Medium
A nucleus disintegrates into two smaller parts, which have their velocities in the ratio $3:2$. The ratio of their nuclear sizes will be $\left(\dfrac x3\right)^{1/3}$. The value of $x$ is ______.
Numerical value type. Enter your answer.
Answer: 2
Momentum conservation: $m_1v_1=m_2v_2\Rightarrow\dfrac{m_1}{m_2}=\dfrac{2}{3}$.
$R\propto A^{1/3}$, so $\dfrac{R_1}{R_2}=\left(\dfrac23\right)^{1/3}$ and $x=2$.
Solution by Sreeraj P, M.Sc Physics