A heavy nucleus at rest breaks into two fragm | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) According to the law of conservation of linear momentum,the initial momentum is zero,so $m_1v_1 = m_2v_2$.This implies $\frac{m_1}{m_2} = \frac{v_

Vedclass · Accepted Answer

$1/2$

Vedclass · Answer

(D) According to the law of conservation of linear momentum,the initial momentum is zero,so $m_1v_1 = m_2v_2$.This implies $\frac{m_1}{m_2} = \frac{v_2}{v_1}$.Given the ratio of velocities $\frac{v_1}{v_2} = \frac{8}{1}$,so $\frac{v_2}{v_1} = \frac{1}{8}$.Assuming the density $\rho$ of the nucleus is constant,the mass $m$ is proportional to the volume,$m = \rho \cdot \frac{4}{3}\pi r^3$.Therefore,$\frac{m_1}{m_2} = \frac{r_1^3}{r_2^3}$.Equating the two expressions: $\frac{r_1^3}{r_2^3} = \frac{v_2}{v_1} = \frac{1}{8}$.Taking the cube root on both sides: $\frac{r_1}{r_2} = \sqrt[3]{\frac{1}{8}} = \frac{1}{2}$.

$A$ heavy nucleus at rest breaks into two fragments which fly off with velocities in the ratio $8 : 1$. Find the ratio of the radii of the fragments.

Similar Questions

Which of the following pairs of nuclei are isobars?

$A$ nucleus splits into two nuclear fragments. If the ratio of their velocities is $2:1$,then the ratio of their nuclear radii is:

$A$ nucleus represented by the symbol ${ }_{Z}^{ A } X$ has

Two nuclei have their mass numbers in the ratio of $1: 3$. The ratio of their nuclear densities would be

On the bombardment of a neutron with Boron,an $\alpha$-particle is emitted. The product nucleus formed is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module