The multiplication of the total mass of a system and the acceleration of its centre of mass denotes what?

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.

Two persons of mass $m_1$ and $m_2$ are standing at the two ends $A$ and $B$ respectively,of a trolley of mass $M$ as shown. When both the persons jump simultaneously with the same speed,then:

State Newton's second law for a system of particles.

Assertion $(A):$ If there is no external torque on a body about its centre of mass,then the velocity of the centre of mass remains constant.
Reason $(R):$ The linear momentum of an isolated system remains constant.

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