A) \[12\text{ }m{{s}^{-1}}\]opposite to heavier mass
B) \[12\text{ }m{{s}^{-1}}\] in the direction of heavier mass
C) \[6\text{ }m{{s}^{-1}}\]opposite to heavier mass
D) \[6\text{ }m{{s}^{-1}}\]in the direction of heavier mass
Correct Answer: A
Solution :
The ratio of masses = 1 : 3 Therefore, \[{{m}_{1}}=x\,kg,{{m}_{2}}=3x\,kg\] Applying law of conservation of momentum \[{{m}_{1}}{{v}_{1}}+{{m}_{2}}{{v}_{2}}=0\] \[\Rightarrow \] \[x\times {{v}_{1}}+3x\times 4=0\] \[\Rightarrow \] \[{{v}_{1}}=-12m/s\] Therefore, velocity of lighter mass is opposite to that of heavier mass.
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