Question

In the system shown in figure $m_B=4kg$, and $m_A=2kg$. The pulleys are massless and friction is absent everywhere The acceleration of block $A$ is

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

Answer 1

Answer: (A)

For movable pulley

$a_B=\frac{O+a_A}{2}$

$a_A=2a_B\dots (i)$

Free body diagrams of $A$ and $B$ :



Equation of motion of blocks $A$ and $B$

For A: $T-\frac{m_{A}g}{2}=m_A{a}_A=m_A\left(2a_B\right)\dots \left(ii\right)$

For B:$m_{B}g-2T=m_B{a}_B\dots \left(iii\right)$

From $\left(ii\right)$ and $\left(iii\right)\left[2\left(ii\right)+\left(iii\right)\right]$

$m_{B}g-m_{A}g=\left[4m_A+m_B\right]a_B$

$\Rightarrow a_B=\frac{\left[m_B-m_A\right]g}{\left[4m_A+m_B\right]}$

$=\frac{\left[4-2\right]\times 10}{\left[4\times 2+4\right]}$

$=\frac{20}{12}=\frac{5}{3}m{s}^2$

Hence $a_A=2a_B=\frac{10}{3}m/s^2$