In the figure given below, with what acceleration does the block of mass $m$ will move?
(Pulley and strings are massless and frictionless)

\frac{g}{3}

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\frac{2 g}{5}

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\frac{2 g}{3}

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\frac{g}{2}

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Solution

The correct option is C $\frac{2 g}{3}$
For the single pulley system, $a = (\frac{m_{1} - m_{2}}{m_{1} + m_{2}}) g$
Take $2 m$ and $3 m$ as a single system (i.e., single block of mass $5 m$ )
$m_{1} = 5 m$
$m_{2} = m$
$a = (\frac{5 m - m}{5 m + m}) g = \frac{2 g}{3}$

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