A block of mass $M$ is placed on the top of a bigger block of mass $10M$ as shown in figure. All the surfaces are frictionless. The system is released from rest.

 

 

 

Find the distance moved by the bigger block at the instant when the smaller block reaches the ground. 

If the bigger block moves toward right by a distance $\left(x\right)$ then the smaller block will move toward left by a distance $\left(2.2-x\right)$. 

Now considering both the blocks together as a system, horizontal position of  $CM$ remains same. 

As the sum of mass moments about centre of mass is zero i.e.$\underset{ }{\overset{ }{\sum m_i{x}_{i/cm}}}=0$ 

$M\left(2.2-x\right)=10 Mx\Rightarrow x=0.2 m$