Question

There are some passengers inside a stationary railway compartment. The track is frictionless. 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 along the track.

• A. both $C_1$ and $C_2$ will move with respect to the ground
• B. neither $C_1$ nor $C_2$ will move 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

Answer: (C)

$C_1$ will move but $C_2$ will be stationary with respect to the ground

Given the track is frictionless, therefore as the people inside will move inside the compartment the compartment will itself move opposite to it.
Hence $C_1$ will move but as their is no external force on the combined system and its initial velocity is also zero. Therefore $C_2$ won't change.