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 \[2mg=4ma\] \[\Rightarrow \] \[a=\frac{g}{2}\]