The correct option is C 1.33 m
Take leftward direction as +ve x axis.
Let the distance moved by the bigger block towards right =x m
Then, smaller block will move the distance = (8−x) m towards left side
Given, masses m1=2 kg,m2=10 kg
There is no external force on the system (smaller block + bigger block) in the horizontal (x) direction. Since the center of mass of the system was at rest initially, it will remain at rest in the horizontal direction.
i.e change in x - coordinate of COM of the system, Δxcom=0
Δxcom=m1x1+m2x2m1+m2=0
⇒2×(8−x)+10(−x)2+10=0
⇒16−2x−10x=0
⇒16=12x
⇒x=1.33 m
Distance moved by the bigger block is 1.33 m towards right.