A heavy nucleus at rest breaks into two fragments which fly off with velocities in the ratio $3: 1$. The…
A heavy nucleus at rest breaks into two fragments which fly off with velocities in the ratio $3: 1$. The ratio of radii of the fragments is
$1: 3^{1 / 3}$
$3^{1 / 3}: 4$
$4: 1$
$2: 1$
Solution
From law of conservation of momentum
$\begin{aligned} m v=\text { constant } & \\ V \rho v & =k \\ \frac{4}{3} \pi R^3 \rho v & =k\end{aligned}$
$\left(\frac{R_1}{R_2}\right)^3=\frac{v_2}{v_1} \Rightarrow \frac{R_1}{R_2}=\left(\frac{v_2}{v_1}\right)^{1 / 3}=\left(\frac{1}{3}\right)^{1 / 3}=1: 3^{1 / 3}$