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 : 3^(1/2)`
C. `3^(1/2) : 1`
D. `10^(9) K`

Answer

D

Explanation

Applying conservation of momentum, we get
`m_(1) v_(1) = m_(2) v_(2) rArr (m_(1))/(m_(2)) = (v_(2))/(v_(1)) = (1)/(2)`
Also, `R prop m^(1//3) rArr m prop R^(3)`
`(m_(1))/(m_(2)) = (1)/(2) = ((R_(1))/(R_(2)))^(3) rArr (R_(1))/(R_(2)) = ((1)/(2))^(1//3) = 1 : 2^(1//3)`