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

Question

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 (A) 1: 31/3 (B) 31/3: 4 (C) 4: 1 (D) 2: 1

Tardigrade Admin · Accepted Answer

As the heavy nucleus at rest breaks, therefore according to law of conservation of momentum, we get

m_{1} υ_{1} + m_{2} υ_{2} = 0

or

\frac{υ _{1}}{υ _{2}} = \frac{m _{2}}{m _{1}} = \frac{3}{1} .... (i)

As nuclear density is same,

∴ \frac{m _{2}}{m _{1}} = \frac{ρ \frac{4}{3} π R _{1}^{3}}{ρ \frac{4}{3} π R _{2}^{3}} = \frac{R _{1}^{3}}{R _{2}^{3}}

or

\frac{R _{1}^{3}}{R _{2}^{3}} = \frac{m _{1}}{m _{2}} = \frac{1}{3}

(Using

(i)

)

∴ R_{1} : R_{2} = 1 : 3^{1/3}

Q. 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

$1 : 3^{1/3}$

$3^{1/3} : 4$

$4 : 1$

$2 : 1$

Q. 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

1:31/3

31/3:4

4:1

2:1

$1 : 3^{1/3}$

$3^{1/3} : 4$

$4 : 1$

$2 : 1$