Relation between P, V, T, Gamma in Adiabatic Proceses
A heavy nucle...
Question
A heavy nucleus splits into two fragment nuclei whose surface area are in the ratio 9:25. Ratio of speeds of the two fragments is
A
27:16
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B
64:27
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C
81:16
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D
125:27
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Solution
The correct option is D125:27
Given-* Ratio of surface areas of two nuclei
=9:25
⇒ Ratio of surface area considering them as spherical=4πr214πr22=925
Where r1 and r2 are radius of ⇒r21r22=925⇒r1r2=35 Now, let the density of the nuclei be (p) ⇒ Ratio of their masses →M1M2=ρ⋅43πr31ρ⋅43πr32=27125
* Now by conservation of momentum -M1v1=M2v2v1=speed of nuclei 1v2= speed of nuclei2⇒v1v2=M2M1=12527⇒ Ratio of their velocity is 125:27 Hence, opt (d) is correct.