Thank you for reporting, we will resolve it shortly
Q.
In the system shown in the figure, the acceleration of $1 \,kg$ mass is
Laws of Motion
Solution:
If $a$ is downward acceleration of $4 \,kg$ block, the upward acceleration of $1 \,kg $ block must be $2a$.
Let $T$ be tension in each part of string.
The equation of motion on $4 \,kg$ block is
$4g-2T=4a$ $\quad...\left(i\right)$
The equation of motion on $1 \,kg$ block is
$T-1g$ $=1\times2a$ $... \left(ii\right)$
or $2T$$-2g$ $=4a$ $\ldots\left(iii\right)$
Adding (i) and (iii), we get
$2g$$=8a$ or $a=\frac{g}{4}$
$\therefore $ Acceleration of $1 \,kg$ block $=2a$ $=\frac{g}{2}$ upwards.
