question_answer

The figure shows a pulley mass system which is kept in an elevator moving up with acceleration g. Then the tension T in the string is given by

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 \[{{m}_{2}},\] \[{{m}_{2}}g+{{m}_{2}}g-t={{m}_{2}}a\] \[\Rightarrow \]   \[\frac{T}{{{m}_{1}}}-(2g)=2g-\frac{t}{{{m}_{2}}}\] \[\Rightarrow \]   \[T=\frac{4g\times {{m}_{1}}{{m}_{2}}}{{{m}_{1}}+{{m}_{2}}}\]