A) \[\frac{{{m}_{1}}{{m}_{2}}g}{{{m}_{1}}+{{m}_{2}}}\]
B) \[\frac{2{{m}_{1}}{{m}_{2}}g}{{{m}_{1}}+{{m}_{2}}}\]
C) \[\frac{4{{m}_{1}}{{m}_{2}}g}{{{m}_{1}}+{{m}_{2}}}\]
D) \[\frac{({{m}_{1}}-{{m}_{2}})g}{{{m}_{1}}+{{m}_{2}}}\]
Correct Answer: C
Solution :
[c] Let us solve the question with respect to elevator for. Let acceleration of \[{{m}_{1}}\] with respect to elevator is a upward then acceleration of \[{{m}_{2}}\] with respect to elevator is a down. For \[{{m}_{1}},\] \[T-{{m}_{1}}g-{{m}_{1}}g={{m}_{1}}a\] [considering pseudo force] For \[{{m}_{2}},\] \[{{m}_{2}}g+{{m}_{2}}g-t={{m}_{2}}a\] \[\Rightarrow \] \[\frac{T}{{{m}_{1}}}-(2g)=2g-\frac{t}{{{m}_{2}}}\] \[\Rightarrow \] \[T=\frac{4g\times {{m}_{1}}{{m}_{2}}}{{{m}_{1}}+{{m}_{2}}}\]You need to login to perform this action.
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