Question

A rigid body is dropped from the top of a tower. Midway it splits into two unequal parts. The Centre of mass of the system:

• A. Shifts horizontally towards the heavier part
• B. Shifts horizontally towards the lighter part
• C. Does not shift horizontally
• D. Shifts depending on the velocity at the time of split

Hint:

Think of the center of mass as representing the entire system. When internal forces occur within a system, they have no impact on the center of mass’ trajectory because each internal force has an equal and opposite reaction force, canceling any net force on the center of mass.

Answer 1

The Correct Option is C

The center of mass of a system is the average location of all its mass. The motion of the center of mass of a system is not affected by internal forces (like the force of the rigid body breaking apart); it only changes due to external forces (in this case, gravity). Since gravity acts vertically downward, there is no external horizontal force acting on the system. When the rigid body is falling, it’s accelerating in the vertical direction only because of gravity. When the rigid body splits into two parts, no new horizontal forces are introduced, so there is no reason for the center of mass to move horizontally. Although the individual fragments may move horizontally due to the split, their center of mass will remain in the vertical line of motion and will continue to accelerate downwards due to gravity.