Assuming that both the masses start from rest, the distance travelled by the centre of mass in 2s is (Take\[g=10\text{ }m{{s}^{-2}}\])
A) \[\frac{20}{9}m\]
B) \[\frac{40}{9}m\]
C) \[\frac{2}{3}m\]
D) \[\frac{1}{3}m\]
E) 4m
Correct Answer: A
Solution :
Given \[{{m}_{1}}=1kg,{{m}_{2}}=2kg,g=10\,m{{s}^{-2}}\] \[a=\left( \frac{{{m}_{2}}-{{m}_{1}}}{{{m}_{1}}+{{m}_{2}}} \right)g\] \[=\left( \frac{2-1}{1+2} \right)10=\frac{10}{3}\] \[S=\frac{1}{2}a{{t}^{2}}=\frac{1}{2}\times \frac{10}{3}\times 4=\frac{20}{3}\] \[m=\frac{2\times \frac{20}{3}-1\times \frac{20}{3}}{3}=\frac{20}{9}\]
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