Question

Using constraint method find the relation between accelerations of 1 and 2.

Answer 1

At any instant of time let $x_1$ and $x_2$ be the displacements of 1 and 2 from a fixed line (shown as dotted).
Then, $x_1+x_2=$ constant
or $x_1+x_2=l$ (length of string)
Differentiating with respect to time, we have
$v_1+v_2=0$ or $v_1=v_2$
Again differentiating with respect to time, we get
$a_1+a_2=0$ or $a_1=-a_2$
This is the required relation between $a_1$ and $a_2,$ i.e., accelerations of 1 and 2 are equal but in opposite directions.