question_answer

Two weights \[{{w}_{1}}\] and \[{{w}_{2}}\] are suspended to the two strings on a frictionless pulley. When the pulley is 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 :

Equation of motion for first weight \[T={{m}_{1}}g={{m}_{1}}(g+a)\] \[\Rightarrow \]               \[T-2{{m}_{1}}g={{m}_{1}}a\]                                     ?(1) For second weight \[{{m}_{2}}g-T={{m}_{2}}(a-g)\] \[2{{m}_{2}}g-T={{m}_{2}}a\]                     ?(2) On solving Eqs. (1) and (2) \[T=\frac{4{{m}_{1}}{{m}_{2}}g}{({{m}_{1}}+{{m}_{2}})}\]                    \[=\frac{4{{w}_{1}}{{w}_{2}}}{({{w}_{1}}+{{w}_{2}})}\]