A) \[\frac{g}{4}\]
B) \[\frac{g}{2}\]
C) \[g\]
D) \[2g\]
Correct Answer: A
Solution :
Let the magnitude of acceleration of the block be a. \[a=\frac{3mg-mg}{3m+m}=\frac{g}{2}\] Let the downward direction be positive and upward direction negative. Now, \[{{a}_{cm}}=\frac{{{m}_{1}}{{a}_{1}}+{{m}_{2}}{{a}_{2}}}{{{m}_{1}}+{{m}_{2}}}=\frac{3m\frac{g}{2}-\frac{mg}{2}}{3m+m}\] \[\therefore \] \[{{a}_{cm}}=\frac{mg}{4m}=\frac{g}{4}\] Hence, the correction option is [a].
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