Question

There are some passengers inside a stationary railway compartment. The centre of mass of the compartment itself (without the passengers) is ${C_1}$, while the centre of mass of the compartment plus passengers is ${C_2}$. If the passengers move about inside the compartment then
A. Both ${C_1}$ and ${C_2}$ will move with respect to the ground
B. Neither ${C_1}$ nor ${C_2}$ will be stationary with respect to the ground
C. ${C_1}$ will move but ${C_2}$ will be stationary with respect to the ground
D. ${C_2}$ will move but ${C_1}$ will be stationary with respect to the ground

Answer 1

First let us see what centre of mass is: A location specified relative to an object or system of objects is the centre of mass. It is the average location, weighted according to the masses, of all the parts of the system. We can measure the centre of mass by taking the masses we are seeking to find between the centre of mass and multiplying them by their locations. We then add these together and divide them by the sum of all the masses of people.

Complete answer:
The centre of mass has no fixed point in the human body, it is based at any given moment on the performer's location. The centre of mass in all athletes varies regardless of the body structure, since bone, fat, tissue and muscle all add to overall mass and are in varying proportions of each performer.

If net external force is zero, then the system's centre of mass stays at rest. Thus if the passenger travels inside the compartment and does not require any external force, the centre of mass of the "passenger plus compartment" mechanism must stay at rest and ${C_2}$ would then be fixed on ground.

The location of the centre of mass of the passengers can therefore only change due to the rotation of the passenger, so ${C_1}$ will have to travel in such a way that ${C_2}$ will stay constant with respect to surface.

Hence, option C is correct.

Note: We may be confused between centre of mass and centre of gravity but centre of mass is the distribution of mass and centre of gravity is the distribution of weight. Also centre of mass does not depend on the gravitational field and centre of gravity does.