True or false about the centre of mass

Problem

True or false?

• (a) The centre of mass of an isolated system moves with uniform rectilinear motion.
• (b) The centre of mass of a body must always lie inside the body.
• (c) In a collision, even an inelastic one, the velocity of the centre of mass is conserved.
• (d) A person can accelerate their own centre of mass without the help of external forces.

Solution

$\ev{\text{(a) T}, \quad \text{(b) F}, \quad \text{(c) T}, \quad \text{(d) F}}$

• (a) True. Isolated system $\Rightarrow \sum F_\text{ext} = 0 \Rightarrow \vec{a}_\text{CM} = 0 \Rightarrow \vec{v}_\text{CM}$ constant: uniform rectilinear motion.
• (b) False. The CM of a ring (or a horseshoe) lies at a point where there is no material.
• (c) True. The collision is due to internal forces; $\vec{v}_\text{CM}$ does not change, whether the collision is elastic or inelastic.
• (d) False. To accelerate one’s own CM an external force is needed (the ground, the air, the water). Internal forces alone do not move the centre of gravity.

Links

Topics: Centre of mass Concepts: Centre of mass · Conservation of momentum