A nucleus ruptures into two nuclear parts, which have their velocity ratio equal to `2 : 1`. What will be the ratio of their nuclear size (nuclear radius)?

Options

A. `2^(1//3) : 1`
B. `1: 2^(1//3)`
C. `3^(1//2) : 1`
D. `1: 3^(1//2)`

Answer

B

Explanation

From momentum conservation,
`m_(1)v_(1)= m_(2)v_(2)`
`rArr (m_(1))/(m_(2)) = (v_(2))/(v_(1))= (A_(1))/(A_(2))= (1)/(2)`
`therefore (R_(1))/(R_(2))= ((A_(1))/(A_(2)))^((1)/(3)) = ((1)/(2))^((1)/(3)) rArr (R_(1))/(R_(2))= 1: 2^((1)/(3))`