An unstable heavy nucleus at rest breaks in to two nuclei which move away with velocites oin the ration f 8: 27 The ratio of the radii of the nuclei (assumed to be spherical) is :

Options

A. `8 : 27`
B. `2 : 3`
C. `3 : 2`
D. `4 : 9`

Answer

C

Explanation

Let heavy nucleus breaks into two nuclei of mass `m_(1)` and `m_(2)` and move away with velocities `V_(1)` and `V_(2)` respectively .
According to question , `(V_(1))/(V_(2)) = (8)/(27) m_(1) V_(1) = m_(2) V_(2)` (Law of momentum conservation)
`implies (m_(1))/(m_(2)) = (V_(2))/(V_(1)) = (27)/(8)`
`(rho xx (4)/(3) pi R_(1)^(3))/(rho xx (4)/(3) pi R_(2)^(3)) ( because ` density `rho = ( "mass")/("volume"))`
`implies ((R_(1))/(R_(2))) = ((27)/(8))^((1)/(3)) = ((3)/(2))^(3 xx (1)/(3)) therefore (R_(1))/(R_(2)) = (3)/(2)`