Question

In the figure shown, the acceleration of $A$ is $2m/s^2$ to left and acceleration of $B$ is $1m/s^2$ to left.

The magnitude of acceleration of $C$ in $m/s^2$ is__.

Answer 1

Answer: 1

Let displacement of $A$ is $x_1,B$ is $x_2$ and that of $C$ is $x_3$ in a given time.
Now length of string should remain same.

So initial length $=$ final length
$\Rightarrow l_1+l_2+l_3+l_4+l_5$
$=\left(l_1+x_1-x_2\right)+\left(l_2-x_2\right)+\left(l_3+x_1\right)+\left(l_4+x_3\right)+\left(l_5+x_3\right)$
$\Rightarrow x_3=x_2-x_1$ Differentiating twice:
$a_3=a_2-a_1$
$\Rightarrow a_3=1-2=-1m/s^2$
So acceleration of $C$ is $1m/s^2$ upwards.