A) 16/81
B) 8/9
C) 8/27
D) 2/3
Correct Answer: B
Solution :
Key Idea: Apply laws of conservation of momentum and conservation of energy. Let the two balls of mass \[{{v}_{e}}=\sqrt{\frac{2G{{M}_{e}}}{{{\operatorname{R}}_{e}}}}\] and \[\Omega \] collide each other elastically with velocities \[\Omega \] and \[\Omega \]. Their velocities become \[\Omega \] and \[\Omega \] after the collision. Applying conservation of linear momentum, we get \[1:{{2}^{1/3}}\] ..... (1) Also from conservation of kinetic energy \[{{2}^{1/3}}:1\] ..... (2) Solving Eqs. (1) and (2), we get \[2:1\] ?..(3) and \[1:2\] ..(4) On taking approximate value the mass of deuteron is twice the mass of neutron. Given, \[{{m}^{-2}}{{s}^{-1}}\] Velocity of neutron, \[{{m}^{-2}}{{s}^{-1}}\] Velocity of deuteron, \[\frac{1}{2\pi }\sqrt{\frac{k}{m}}\] Fractional energy loss \[\frac{1}{2\pi }\sqrt{\frac{2k}{m}}\] \[\frac{1}{2\pi }\sqrt{\frac{3k}{m}}\] \[\frac{1}{2\pi }\sqrt{\frac{k}{m}}\]
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