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A nucleus disintegrates into two nuclear parts which have their velocities in the ratio 2:1. The ratio of their nuclear sizes will be

Asked in JEE Main 2004 · Nuclear radius and density

(1) 2^1/3:1
(2) 1:3^1/2
(3) 3^1/2:1
(4) 1:2^1/3

Answer: (4) 1:2^1/3

Step-by-step solution

m₁v₁=m₂v₂: (m₁)/(m₂)=1/2.

(R₁)/(R₂)=(1/2)^1/3=1:2^1/3

Why the other options are wrong

(1) Takes mass proportional to speed.
(2) Uses a square root.
(3) Uses a square root.

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