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)                 \[3mg-T=3ma\]                                 ... (ii) Adding Eqs. (i) and (ii), we get                 \[2mg=4ma\] \[\Rightarrow \]                     \[a=\frac{g}{2}\]