ROTATIONAL MOTION

How does the center of mass of a homogeneous disc compare to its geometric center?

• The center of mass is at the edge
• The center of mass is outside
• The center of mass is at a random point
• They are identical

What is the role of the origin in calculating ∫ x dm?

• It has no role
• It doubles the integral
• It eliminates mass
• It determines the reference point for position measurement

In the expression X = (1/M) ∫ x dm, what does M represent?

• Mass of a single element
• Mass per unit length
• Moment of inertia
• Total mass of the body

For a homogeneous ring, why is the center of mass at the center despite no mass being there?

• Because the ring is empty
• Because gravity pulls from center
• Because it is lighter at edges
• Due to circular symmetry and balanced mass distribution

How does reflection symmetry help in determining the center of mass of a rod?

• It doubles the mass
• It shifts the center to one end
• It increases the length
• It ensures that contributions from symmetric elements cancel