Question

In the system shown in figure $m_{B}= 4 \,kg$, and $m_{A} = 2 \,kg$. The pulleys are massless and friction is absent everywhere The acceleration of block $A$ is

• A. $10/3 \,m/s^{2}$
• B. $20/3\,m/s^{2}$
• C. $2\,m/s^{2}$
• D. $4\,m/s^{2}$

Answer 1

Answer: (A)

For movable pulley
$a_{B}=\frac{O+a_{A}}{2}$
$a_{A}=2a_{B} \ldots (i)$
Free body diagrams of $A$ and $B$ :

Equation of motion of blocks $A$ and $B$
For A: $T-\frac{m_{A}g}{2}=m_{A}a_{A}=m_{A}\left(2a_{B}\right) \ldots \left(ii\right)$
For B:$m_{B}g-2T=m_{B}a_{B} \ldots \left(iii\right)$
From $\left(ii\right)$ and $\left(iii\right) \left[2\left(ii\right) + \left(iii\right)\right]$
$m_{B}g-m_{A}g=\left[4m_{A}+m_{B}\right]a_{B}$
$\Rightarrow a_{B}=\frac{\left[m_{B}-m_{A}\right]g}{\left[4m_{A}+m_{B}\right]}$
$=\frac{\left[4-2\right]\times10}{\left[4\times2+4\right]}$
$=\frac{20}{12}=\frac{5}{3}m s^{2}$
Hence $a_{A}=2a_{B}=\frac{10}{3} \,m /s^{2}$