The system shown in figure is released from rest. Find acceleration of different blocks and tension in different strings.

(i) Pulley P and 1kg mass are attached with the same string. Therefore, if 1kg mass hat acceleration ' a' in upward direction, then pulley P will have an acceleration ' a ' downwards.

 (ii) 2kg and 3kg blocks are attached with the same string passing over a moveable pulley p. Therefore, their relative acceleration, $a_r$ (relative to pulley) will be same. Their net accelerations (relative to ground) are as shown in figure.

(iii) Pulley P is massless. Hence net force on this pulley should be zero. If T is the tension in the string connecting 2kg and 3kg mass, then tension in the upper string will be 2 T. Now writing the equation, $F_{\text{net }}=ma$ for three blocks, we have:

1kg block: 

2kg block: 

3 kg block:

Solving Eqations (i), (ii) and (iii) we get,

T=828N

$a=6.55 \mathrm{m}/{\mathrm{s}}^2 \text{ and } a_r=0.7 \mathrm{m}/{\mathrm{s}}^2\text{. }$

Now, acceleration of 3kg block is $\left(a+a_r\right)$ or $7.25 \mathrm{m}/{\mathrm{s}}^2$downwards and acceleration of $2 \mathrm{kg}$ block is $\left(a_r-a\right)$ or $-585 \mathrm{m}/{\mathrm{s}}^2$ upwards. Since, this comes out to be negative, hence acceleration of $2 \mathrm{kg}$ block is $5.85 \mathrm{m}/{\mathrm{s}}^2$downwards.