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

Law of conservation of linear momentum
`m_(1)v_(1)= m_(2) v_(2) rArr (v_(1))/(v_(2)) = 8= (m_(2))/(m_(1)) = (A_(2))/(A_(1))`
Now, `R= R_(0) A^((1)/(3))`
`(R_(1))/(R_(2)) = ((A_(1))/(A_(2)))^((1)/(3)) = ((1)/(8))^((1)/(3)) = (1)/(2)`