question_answer

Two weights\[{{w}_{1}}\]and\[{{w}_{2}}\]are suspended to be the two strings on a frictionless pulley. When the pulled up with an acceleration\[g\]then the tension in the string is

A) \[\frac{4{{w}_{1}}{{w}_{2}}}{{{w}_{1}}+{{w}_{2}}}\]                        

B) \[\frac{{{w}_{1}}{{w}_{2}}}{{{w}_{1}}+{{w}_{2}}}\]

C) \[\frac{2{{w}_{1}}{{w}_{2}}}{{{w}_{1}}+{{w}_{2}}}\]        

D)        \[\frac{{{w}_{1}}+{{w}_{2}}}{2}\]

Correct Answer: A

Solution :

The free body diagram of the given situation is shown. Taking the upward and downward motions respectively, we get                 \[{{T}_{1}}-mg={{m}_{1}}(g+a)\]                 \[T-2mg={{m}_{1}}a\] for second weight                 \[{{m}_{2}}g-T={{m}_{2}}(g-a)\]                 \[2{{m}_{2}}g-T={{m}_{2}}a\]                 \[T=\frac{4{{m}_{1}}{{m}_{2}}g}{({{m}_{1}}+{{m}_{2}})}\] \[{{w}_{1}}={{m}_{1}}g,\,\,{{m}_{2}}={{m}_{2}}g\]hence switch                 \[T=\frac{4{{w}_{1}}{{w}_{2}}}{({{w}_{1}}+{{w}_{2}})}\]