A nucleus ruptures into two nuclear parts which have heir velocity ratio equal to 2: 1 . The ratio of their respective nuclear sizes (nuclear radii) is

Question

A nucleus ruptures into two nuclear parts which have heir velocity ratio equal to 2: 1 . The ratio of their respective nuclear sizes (nuclear radii) is (A) 1: 2 (B) 1: √2 (C) 1: 21 / 3 (D) 1: 8

Tardigrade Admin · Accepted Answer

Conserving momentum, m1 v1=m2 v2 (2/1)=(v1/v2)=(m2/m1) ⇒ (m2/m1)=(2/1)=(ρ ⋅ (4/3) π r23/ρ ⋅ (4)3 π r13) ⇒ (r2/r1)=2(1/3) or r1: r2=1: 2(1/3)

Q. A nucleus ruptures into two nuclear parts which have heir velocity ratio equal to $2 : 1.$ The ratio of their respective nuclear sizes (nuclear radii) is

1 : 2

$1 : 2$

$1 : 2^{1/3}$

1 : 8

Q. A nucleus ruptures into two nuclear parts which have heir velocity ratio equal to 2:1. The ratio of their respective nuclear sizes (nuclear radii) is

1 : 2

1:2​

1:21/3

1 : 8

Conserving momentum, m1​v1​=m2​v2​ 12​=v2​v1​​=m1​m2​​ ⇒m1​m2​​=12​=ρ⋅34​πr13​ρ⋅34​πr23​​ ⇒r1​r2​​=231​ or r1​:r2​=1:231​

Q. A nucleus ruptures into two nuclear parts which have heir velocity ratio equal to $2 : 1.$ The ratio of their respective nuclear sizes (nuclear radii) is

$1 : 2$

$1 : 2^{1/3}$