question_answer

A pulley fixed to the ceiling carries a string with  blocks of masses \[m\] and\[3m\] attached to its ends. The masses of string and pulley are negligible. When the system is released, the acceleration of centre of mass will be

A)  Zero

B)  \[-\frac{g}{4}\]

C)  \[\frac{g}{2}\]

D)  \[-\frac{g}{2}\]

Correct Answer: C

Solution :

  Let T be the tension in the string carrying the masses \[m\]and \[3m.\] Let a be the acceleration, then \[T-mg=ma\] ?(i) \[2mg-T=3ma\] ?(ii) Adding Eqs. (i) and (ii), we get \[2mg=4ma\] \[\Rightarrow \] \[a=\frac{g}{2}\]