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 $8\text{kg}$
$2T=8a_2...\left(1\right)$
For $4\text{kg}$ block
$4g-T=4a_1...\left(2\right)$
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 $a_1/2$.
Hence, $a_2=a_1/2...\left(3\right)$
Substituting in equations $\left(i\right)\&\left(ii\right),$ we get

add eq(1) and 2*eq(2)

$a_1=\frac{8g}{12}=\frac{2g}{3}$

$a_1=2g/3$

using eq(3) we get
$a_2=g/3$