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# Two blocks of masses $6\; kg$ and $4\;kg$ are attached to the two ends of a massless string passing over a smooth fixed pulley. If the system is released, the acceleration of the centre of mass of the system will be ;

$\begin{array}{1 1} a) g_1\; vertically\; downwards \\ b) \frac{g}{5}, vertically\; downwards \\ c) \frac{g}{25}, vertically\; downwards \\ d) zero \end{array}$

$a_{system}=\bigg(\large\frac{6-4}{10}\bigg)$$g=\large\frac{g}{5}$$m/s^2$
$\bar{a}_{cm}=\Large\frac{m_1\bar {a_1}+m_2 \bar {a_2}}{m_1+m_2}$
$\qquad=\large\frac{6 \times \Large\frac{g}{5}-4 \times \frac{g}{5}}{10}$
$\qquad= \large\frac{g}{25}$
Vertically downwards

Hence (c) is the right answer.

edited Dec 14, 2013 by pady_1