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Question

A nucleus at rest splits into two nuclear parts having same density and radii in the ratio 1:2. Their velocities are in the ratio


A

2:1

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B

4:1

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C

6:1

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D

8:1

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Solution

The correct option is D

8:1


Let, the mass of a part of the nucleus be m=ρv=ρx43πr3 [Where, m is the mass, ρ is density, v is the volume of nucleus, r is the radius of the nucleus.]

Applying the law of conservation of momentum,

m1v1=m2v2 [m1,m2 are the masses of the split part of the nucleus, v1,v2 are the volumes of the spit part of the nucleus.]

[ρx(4/3)πr13]v1=[ρx(4/3)πr23]v2v1v2=r2r13v1v2=213v1v2=81[Where, the ratio of the split part of the nucleus r1r2=12]

Their velocities are in the ratio 8:1.

Hence, option D is correct.


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