Question

Find the acceleration of block $B$ in the shown figure.

• A. $2{\text{m/s}}^2$, leftward
• B. $\frac{4}{3}{\text{m/s}}^2$, leftward
• C. $\frac{2}{3}{\text{m/s}}^2$, leftward
• D. $3{\text{m/s}}^2$, rightward

Answer 1

The correct option is B $\frac{4}{3}{\text{m/s}}^2$, leftward

Let us assume that the block $B$ moves leftward with an acceleration of $a$ and taking leftward positive we have

Now considering the different points starting from $1$ to $5$ as shown in the figure, we can have
$-a+a_A+a_A-a-a=0$
$\Rightarrow 3a=2a_A=2\times 2=4\Rightarrow a=\frac{4}{3}{\text{m/s}}^2$
Hence, the acceleration of block $B$ is $a=\frac{4}{3}{\text{m/s}}^2$, leftward.