A) \[\frac{g}{8}\]
B) \[\frac{g}{2}\]
C) \[\frac{g}{4}\]
D) g
Correct Answer: B
Solution :
[b]| \[a=b+c\] [string constrained] |
| \[T={{m}_{B}}b\] [Newton's II law for B in horizontal direction] |
| \[T=[{{m}_{A}}+{{m}_{C}}]c\] [Newton's I law for A and C in horizontal direction] |
| \[{{m}_{A}}g-T={{m}_{A}}a\] [Newton's I law for A and C in horizontal direction] |
| \[\frac{{{m}_{A}}g-T}{{{m}_{A}}}=\frac{T}{{{m}_{B}}}+\frac{T}{{{m}_{A}}+{{m}_{C}}}\] |
| \[\frac{4mg-T}{4m}=\frac{T}{3m}+\frac{T}{12m}\] |
| \[\Rightarrow \] \[T=\frac{3mg}{2}\Rightarrow b=\frac{g}{2}\] |
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