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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