A cart carries two blocks of mass $2 kg$ and $1 kg$ which are connected by a string passing over a pulley. The cart is moving towards right with an acceleration of $1 m/s^2$ . Find acceleration of blocks with respect to ground and tension in the string. (Take $g=10m/s^2$)

 

Let acceleration of the $2 kg$ block is $a$ towards right with respect to cart. The forces on the blocks in accelerated frame. The forces mark by dotted arrows are pseudo forces.

For $2 kg$ block; $T - 2\times 1=2a$         …(i)

For $1 kg$ block; $1g - T = 1a$           …(ii)

Solving equations (i) and (ii), we get

   $a=\frac{8}{3}m/s^2 and T = \frac{22}{3}N$ .

Acceleration of blocks w.r.t. ground;

Acceleration of $1 kg$ block $=\frac{8}{3}m/s^2$ along downward and $1 m/s^2$ along horizontal

Acceleration of  $2 kg$ block; $a=\frac{8}{3}+1=\frac{11}{3}m/s^2$ .