Shift in Centre of Mass When certain mass is Removed

If a certain mass from the system is removed, center of mass obviously changes from its existing position. When some mass of the system is removed, new center of mass shifts towards the heavier part of the system.

We know that center of mass of a system is a point of a system that represents the actual motion of a system when some external force is applied on the system.For a geometrically symmetric body, center of mass is at its geometrical center and it even coincides with center of gravity.

We can use the basic principle of center of mass in solving this conceptual problem to derive a mathematical equation. We know that the algebraic sum of moments about center of mass of the system is always equal to zero. It means the moments of the system about one direction is equal in magnitude and opposite in direction to the moments of the same system in the opposite direction.

Let the original center of mass of the system is at O. Let a small mass is removed from the system whose center of mass is at one point and the remaining portion of the system has center of mass at some other point. We can equate the moment of the system that has two masses. They are removed mass and remaining mass.

By simplifying the above equation, as shown in the below video lesson, we can the location of new center of mass of the system. We can find the shift in the center of mass as the product of mass removed and the distance between original center of mass and removed center of mass divided by the mass of the remaining portion.