A) \[\frac{15}{16}\]
B) \[\frac{1}{2}\]
C) \[\frac{2}{1}\]
D) None of these
Correct Answer: D
Solution :
Neutron velocity = v, mass = m Deuteron contains 1 neutron and 1 proton, mass = 2m In elastic collision both momentum and K.E. are conserved pi = pf mv = m1v2 + m2v2 Þ mv = mv1 + 2mv2 ... (i) By conservation of kinetic energy \[\frac{1}{2}m{{v}^{2}}=\frac{1}{2}mv_{1}^{2}+\frac{1}{2}(2m)v_{2}^{2}\] ... (ii) By solving (i) and (ii) we get \[{{v}_{1}}=\frac{{{m}_{1}}-{{m}_{2}}}{{{m}_{1}}+{{m}_{2}}}v+\frac{2{{m}_{2}}}{({{m}_{1}}+{{m}_{2}})}v\] Þ \[{{v}_{1}}=\frac{{{m}_{1}}+2m}{3m}\]\[=-\frac{v}{3}\] \[{{K}_{i}}=\frac{1}{2}m{{v}^{2}}\], \[{{K}_{f}}=\frac{1}{2}mv_{1}^{2}\] \[\Rightarrow \frac{{{K}_{i}}-{{K}_{f}}}{{{K}_{i}}}=1-\frac{v_{1}^{2}}{{{v}^{2}}}\] \[=1-\frac{1}{9}=\frac{8}{9}\] (Fractional change in K.E.)You need to login to perform this action.
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