Center of Mass

A multi-stage rocket separates into two distinct parts during flight. Assuming no external forces act on the system, what happens to the center of mass of the entire system (both parts combined)?

• It shifts towards the heavier stage.

• It shifts towards the lighter stage.

• It remains at its original location and continues its previous motion.

• It ceases to exist as a single point.

What is the primary characteristic of an object's center of mass when no net external force acts upon it?

• It always remains stationary.

• It moves with a constant velocity.

• It undergoes irregular, unpredictable motion.

• It rotates around a fixed point within the object.

Which experimental method can be used to locate the center of mass of an irregularly shaped, flat object?

• Balancing the object on a single point until it remains stable.

• Submerging the object in water and observing its buoyancy.

• Hanging the object from multiple points and finding the intersection of vertical lines.

• Measuring the object's dimensions and calculating the geometric center.

When observing an object undergoing both translational and rotational motion, why might the overall motion appear complex to an observer?

• The object's mass is constantly changing.

• The observer is not moving with the object.

• The individual parts of the object are moving irregularly relative to the center of mass.

• External forces are continuously acting on the object.

A system of particles experiences various internal forces but no net external force. What can be concluded about the motion of the system's center of mass?

• It will accelerate in the direction of the strongest internal force.

• It will remain stationary regardless of internal motion.

• It will move with a constant velocity.

• Its motion cannot be predicted without knowing the individual particle trajectories.

Which of the following formulas correctly represents the x-coordinate of the center of mass (Xcm) for a system of two masses, m1 and m2, located at positions x1 and x2 respectively?

• Xcm = (m1 + m2) / (m1x1 + m2x2)

• Xcm = (m1x1 + m2x2) / (x1 + x2)

• Xcm = (m1x1 + m2x2) / (m1 + m2)

• Xcm = (m1 + m2) * (x1 + x2)

Consider a system with a 1 kg mass located at 2 meters and a 2 kg mass located at 5 meters from a reference point. What is the x-coordinate of the center of mass for this system?

• 3 meters

• 3.5 meters

• 4 meters

• 4.5 meters

To calculate the center of mass for a system of particles distributed in a two-dimensional plane, what additional information is required beyond the masses and x-coordinates of each particle?

• The velocity of each particle.

• The acceleration of each particle.

• The y-coordinate of each particle.

• The kinetic energy of each particle.