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 \[{{m}_{1}},\] \[T-{{m}_{1}}g={{m}_{1}}{{a}_{1}}\] \[\Rightarrow \] \[{{a}_{1}}=\frac{2{{m}_{1}}g-{{m}_{1}}g}{{{m}_{1}}}=g\] \[{{a}_{cm}}=\frac{{{m}_{1}}{{a}_{1}}+{{m}_{2}}{{a}_{2}}}{{{m}_{1}}+{{m}_{2}}}=\frac{{{m}_{1}}{{a}_{1}}+0}{{{m}_{1}}+{{m}_{2}}}=\frac{{{m}_{1}}g}{{{m}_{1}}+3{{m}_{1}}}=\frac{g}{4}\]