A) \[\frac{{{\lambda }_{A}}}{{{\lambda }_{B}}}=\frac{2}{3}\]
B) \[\frac{{{\lambda }_{A}}}{{{\lambda }_{B}}}=\frac{1}{3}\]
C) \[\frac{{{\lambda }_{A}}}{{{\lambda }_{B}}}=\frac{1}{3}\]
D) \[\frac{{{\lambda }_{A}}}{{{\lambda }_{_{B}}}}=2\]
Correct Answer: D
Solution :
By conservation of linear momentum \[mv=m{{v}_{1}}+\frac{m}{2}{{v}_{2}}\] \[2v=2{{v}_{1}}+{{v}_{2}}\] ?. by law of collision \[e=\frac{{{v}_{2}}-{{v}_{1}}}{{{u}_{1}}-{{u}_{2}}}\] \[u={{v}_{2}}-{{v}_{1}}\] ?. By equation [a] and [b] \[{{v}_{1}}=\frac{v}{3};\] \[{{v}_{2}}=\frac{4v}{3}\] \[{{\lambda }_{1}}=\frac{h}{{{p}_{1}}};\] \[{{\lambda }_{2}}=\frac{h}{{{o}_{2}}}\] \[\frac{{{\lambda }_{1}}}{{{\lambda }_{2}}}=\frac{2}{1}\] Option [d]You need to login to perform this action.
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