Why do internal forces acting within a system not affect its motion?

Two spheres of masses $2M$ and $M$ are initially at rest at a distance $R$ apart. Due to mutual force of attraction,they approach each other. When they are at a separation $R/2$,the acceleration of the centre of mass of the system would be ....... $m/s^2$.

When a bomb explodes during projectile motion,which forces do not contribute to the motion of the centre of mass?

If the total external forces on the system of particles is zero,then find the velocity and acceleration of its centre of mass.

Which types of forces act on a system of particles?

Choose the correct statement$(s)$:
$(A)$ The position of the centre of mass of a system is dependent on the choice of coordinate system.
$(B)$ Newton's second law of motion is applicable to the centre of mass of the system.
$(C)$ Internal forces cannot change the state of the centre of mass.
$(D)$ Internal forces can change the state of the centre of mass.