Two objects, one having twice the mass of the other, are initially at rest. Two forces, one twice as big as the other, act on the objects in opposite directions as shown above.1)Which of the following statements about the acceleration of the center of mass of the system is true?a. a = F/M to the rightb. a = F/(3M) to the rightc. a = 0d. a = F/(3M) to the lefte. a = F/M to the left

When several forces are applied to a particle or a system of particles, the net force is the sum of them all, considering each force as a vector. As for the second Newton's law, the total force equals the product of the mass by the acceleration of the system:

[tex]\vec F_n=m\cdot \vec a[/tex]

If the net force is zero, then the system of particles keeps at rest or at a constant velocity.

The system of particles described in the question consists of two objects of masses m1=M and m2, where

[tex]m_2=2m_1=2M[/tex]

Two forces F1=F and F2 act individually on each object in opposite directions and

[tex]F_2=2F_1=2F[/tex]

We don't get to see any image to know where the forces are applied to, so we'll assume F2 to the right and F1 to the left.

The net force of the system of particles is

[tex]F_n=2F-F=F[/tex]

The mass of the system is

[tex]m_t=m_1+m_2=3M[/tex]

Thus, the acceleration of the center of mass of the system is

[tex]\displaystyle a=\frac{F}{3M}[/tex]

Since F2 is greater than F1, the direction of the acceleration is to the right.

Note: If the forces were opposite than assumed, the acceleration would be to the left