Question

In the figure given below, with what acceleration does the block of mass $2m$ move? (Pulley and strings are massless and frictionless)

• A. $\frac{g}{3}$
• B. $\frac{2g}{5}$
• C. $\frac{2g}{3}$
• D. $\frac{7g}{3}$

Answer 1

The correct option is C $\frac{2g}{3}$

For the single pulley system, $a=\left(\frac{m_1-m_2}{m_1+m_2}\right)g$
Take $2m$ and $3m$ as a single system (i.e. single block of mass $5m$)
Then, $m_1=5m$ & $m_2=m$
Substituting in the above equation,
$a=\left(\frac{5m-m}{5m+m}\right)g=\frac{2g}{3}$