question_answer

Two blocks are resting on ground with masses \[{{m}_{1}}\] and \[{{m}_{2}}\]. A string connects them which goes over a mass less pulley\[P\]. There is no friction between pulley and string. A force \[F\] is applied on pulley\[P\]. The acceleration of centre of mass of blocks is (Given that\[T=2{{m}_{1}}g\]and\[{{m}_{2}}=3{{m}_{1}}\])

A) \[g/8\]                                 

B) \[g/4\]

C) \[\frac{g}{2}\]                                   

D)  \[g\]

Correct Answer: B

Solution :

According to the question,                 \[T=2{{m}_{1}}g\] Thus, \[{{m}_{2}}\]will not be lifted. Hence, its acceleration\[{{a}_{2}}=0\] For\[{{m}_{1}}\],                              \[T-{{m}_{1}}g={{m}_{1}}{{a}_{1}}\] \[\Rightarrow \]                               \[{{a}_{1}}=\frac{2{{m}_{1}}g-{{m}_{1}}g}{{{m}_{1}}}=g\] \[{{a}_{cm}}=\frac{{{m}_{1}}{{a}_{1}}+{{m}_{2}}{{a}_{2}}}{{{m}_{1}}+{{m}_{2}}}=\frac{{{m}_{1}}{{a}_{1}}+0}{{{m}_{1}}+{{m}_{2}}}=\frac{{{m}_{1}}g}{{{m}_{1}}+3{{m}_{1}}}=\frac{g}{4}\]