A nucleus splits into two nuclear parts having radii in the ratio `1:2` Their velocities are in the ratio

Answer

A

Explanation

Let `A_(1) and A_(2)` be the mass number of the two nuclear parts. Their radii are given by
`R_(1)=R_(0)(A_(1))^(1//3) and R_(2)=R_(0)(A_(2))^(1//3)`
Dividing, we get
`(R_(1))/(R_(2))=((A_(1))/(A_(2)))^(1//3) or (A_(1))/(A_(2))=((R_(1))/(R_(2)))^(3)=((1)/(2))^(3)=(1)/(8)`
Hence, the ratio of their masses is
`(m_(1))/(m_(2))=(1)/(8)`
From the principle of conservation of momentum, the magnitude of `p_(1)=` magnitude of `p_(2)=` magnitude of `p_(2)` or `m_(1)v_(1)=m_(2)v_(2)`, which gives `(v_(1))/(v_(2))=(m_(2))/(m_(1))=(8)/(1)`