Question

If pulleys shown in the diagram are smooth and massless and $a_1$ & $a_2$ are acceleration of blocks of mass $4\text{kg}$ and $8\text{kg}$ respectively. Then find $a_2$.

• A. $g/3$
• B. $2g/3$
• C. $4g/3$
• D. $2g$

Answer 1

The correct option is B $2g/3$


For $8\text{kg}$
$2T=8a_2...\left(i\right)$
For $4\text{kg}$ block
$4g-T=4a_1...\left(ii\right)$
From the diagram, we can observe if $4\text{kg}$ moves with acceleration $a_1$ then block of $8\text{kg}$ will move with acceleration $2a_1$.
Hence, $a_2=2a_1...\left(iii\right)$
Substituting in equations $\left(i\right)\&\left(ii\right),$ we get
$a_1=g/3$
$a_2=2g/3$