Final answer:
The acceleration of the center of mass of a system of two particles projected vertically upwards is equal to the gravitational acceleration, g.
Step-by-step explanation:
The question asks about the acceleration of the center of mass of a two-particle system where each particle is projected vertically upwards with different speeds. The key principle involved here is Newton's second law applied to the center of mass, combined with the fact that both particles are subject to the same gravitational acceleration downward, g.
Given that there are no external forces in the y-direction other than gravity acting on both masses, the acceleration of the center of mass is simply the acceleration due to gravity, g. No matter the initial velocities or masses of the particles, gravity affects all parts of the system equally, so the center of mass will accelerate downward at g. The correct answer does not involve the initial velocities or masses directly, so the answer is a) g.
The acceleration of the center of mass of a system can be calculated using the equation:
a = (m1v1 + m2v2) / (m1 + m2)
where m1 and m2 are the masses of the particles, and v1 and v2 are their respective speeds. Therefore, the correct option is (b) (m1v1 + m2v2) / (m1 + m2).