Statements :
a) Motion of centre of mass depends on external forces applied on it .
b) The motion of the centre of mass of the body is called the translational motion of the body.

For a system of particles , if $F_{ext}$ be the resultant external force acting on the system , then

$F_{ext}=m.a_c$ . Internal forces may be there inside the system , but they are action - reaction pairs and cancel each other . So statement - (a) is correct.

When a system undergoes translational motion , its COM must move along a line straight or curved . So statement (b) is true.