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

Options

A. `1 : 2`
B. `1:4`
C. `4:1`
D. `2:1`

Answer

A

Explanation

By conservation of momentum, `m_(1)v_(1)=m_(2)v_(2)`
`implies " "(v_(1))/(v_(2))=8/1=(m_(2))/(m_(1))" "...(i)`
Also, from `r propA^(1//3),`
`therefore" "(r_(1))/(r_(2))=((A_(1))/(A_(2)))^(1//3)=((1)/(8))^(1//3)=1/2`