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' system 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

The correct option is C $C_1$ will move but $C_2$ will be stationary with respect to the ground

When net $F_{external}=0$, then the centre of mass of the system remains at rest.

Thus if the passenger move about inside the compartment which donot require any external force, so the centre of mass of the "passenger + compartment" system must remain at rest and hence $C_2$ will be fixed w.r.t ground.

Also due to the movement of the passenger, the position of centre of mass of the passengers only will change, thus $C_1$ will have to move in such a way that $C_2$ may remain fixed w.r.t ground.