A heavy nucleus at rest breaks into two fragments which fly off with velocities in the ratio 3: 1. The ratio of radii of the fragments is,

Options

A. `1:3^(1/3)`
B. `3^(1/3):4`
C. `4:1`
D. `2:1`

Answer

A

Explanation

From the law of conservation of Momentum,
`m_(1)v_(1) = m_(2)v_(2)`
`v_(1):v_(2) = 3 : 1`
`v_(1)/v_(2) = 3/1 = m_(2)/m_(1)`
` m_(2)/m_(1) = 1/3 = A_(1)/A_(2)`
`R alpha (A)^(1/3)`
`R_(1)/R_(2) = (A_(1)/A_(2))^(1/3)`
`=(1/3)^(1/3)`
`:. R_(1):R_(2) = 1:3^(1/3).`