Centre of Mass — Prelims Strategy

Prelims Strategy

To effectively tackle Centre of Mass questions in NEET, a structured approach is essential. \n1. Coordinate System Selection: Always choose a convenient coordinate system. Placing the origin at one of the particles or at a point of symmetry can significantly simplify calculations, especially for discrete particle systems or composite bodies.

\n2. Discrete Particles: For multiple particles, clearly list their masses and coordinates. Apply the formulas $X_{CM} = \frac{\sum m_i x_i}{\sum m_i}$ and similarly for Y and Z. Be meticulous with arithmetic and signs.

\n3. Composite Bodies (with/without holes): Break down the complex body into simpler, standard shapes whose CoM is known. For bodies with holes, use the 'negative mass' concept: treat the hole as a body of negative mass placed at its own CoM.

Then apply the discrete particle formula. \n4. Continuous Bodies: Memorize the CoM formulas for common uniform shapes (e.g., rod, ring, disc, sphere, hemisphere, cone, semicircular arc/plate). If density varies, be prepared for basic integration ($X_{CM} = \frac{\int x \,dm}{\int dm}$).

\n5. Motion of CoM: Remember the golden rule: $\vec{F}_{ext, net} = M \vec{A}_{CM}$. If external forces are zero, $\vec{V}_{CM}$ is constant. This is vital for collision and explosion problems. For problems involving relative motion (e.

g., man on a boat), conservation of CoM position is the key. \n6. Conceptual Questions: Understand the distinction between CoM and CoG, and when CoM can lie outside the body. \n7. Trap Options: Be wary of options that represent the geometric center (if masses are unequal), or incorrect directions of CoM shift.

Always double-check your calculations and the physical interpretation of your answer.