A) \[1:5\]
B) \[5:1\]
C) \[5:2\]
D) \[2:5\]
Correct Answer: B
Solution :
In elastic collision \[{{v}_{1}}=\left( \frac{{{m}_{1}}-{{m}_{2}}}{{{m}_{1}}+{{m}_{2}}} \right){{u}_{1}}+\left( \frac{2{{m}_{2}}}{{{m}_{1}}+{{m}_{2}}} \right){{u}_{2}}\] If the second ball is at rest, ie, \[{{u}_{2}}=0,\] then \[{{v}_{1}}=\left( \frac{{{m}_{1}}-{{m}_{2}}}{{{m}_{1}}+{{m}_{2}}} \right){{u}_{1}}\] Given, \[{{v}_{1}}=\frac{2}{3}{{u}_{1}}\] \[\frac{2}{3}{{u}_{1}}=\left( \frac{{{m}_{1}}-{{m}_{2}}}{{{m}_{1}}+{{m}_{2}}} \right){{u}_{1}}\] \[\Rightarrow \] \[2{{m}_{1}}+2{{m}_{2}}=3{{m}_{1}}-3{{m}_{2}}\] \[\Rightarrow \] \[{{m}_{1}}=5{{m}_{2}}\] \[\Rightarrow \] \[\frac{{{m}_{1}}}{{{m}_{2}}}=\frac{5}{1}\]
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