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A nucleus at rest splits into two nuclear parts having radii in the ratio of 1:3. Find the ratio of their velocities.(a) 1:9(b) 3:1(c) 1:27(d) 27:1I had been asked this question by my school teacher while I was bunking the class.Asked question is from Size of the Nucleus topic in division Nucleus of Physics – Class 12

Answer»

The correct ANSWER is (d) 27:1

To elaborate: Given: R1 = R0 (A1)^1/3 and R2 = R0 (A2)^1/3

\(\frac {R1}{R2} = (\frac {A1}{A2} ) ^{\frac {1}{3}} \) or \( \frac {A1}{A2} = (\frac {R1}{R2} )^3 = (\frac {1}{3} )^3 \)

\( \frac {A1}{A2} = \frac { 1}{27}\)

So, the ratio of their masses is given as:

\( \frac {m1}{m2} = \frac { 1}{27}\)

According to the principle of CONSERVATION of momentum, the magnitude of p1 = magnitude of p2

m1v1 = m2v2

\( \frac {V1}{v2} = \frac {m2}{m1} = \frac {27}{1}\) = 27:1.


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