Question

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. $-\frac {g}{2}$

Answer 1

Answer: (B)

$-\frac {g}{4}$

Answer 2

Let T be the tension in the string carrying the masses m and 3m.
Let a be the acceleration, then
\hspace10mm T-mg=ma \hspace5mm ...(i)
\hspace10mm 3mg-T=3ma \hspace5mm ...(ii)
\hspace10mm 2mg=4ma
\Rightarrow \hspace10mm a= \frac {g}{2}
$a_{cm} = -g/4$