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Q.
In the figure given below, with what acceleration does the block of mass $m$ will move? (Pulley and strings are massless and frictionless)
Laws of Motion
Solution:
For the single pulley system $a=\left(\frac{m_{1}-m_{2}}{m_{1}+m_{2}}\right) g$
take $2\, m$ and $3\, m$ as a system (i.e., single block of $5 m$ mass)
$m_{1}=5\, m$
$m_{2}=m$
$a=\left(\frac{5 m-m}{5 m +m}\right) g=\frac{2 g}{3}$