Physics · System Of Particles And Rotational Motion · NEET
No. They coincide only when the gravitational field g is the same (uniform) over the whole body. For every object you handle in NEET problems on Earth, g is effectively constant, so CM and CG are at the same point. They separate only for very large bodies (like a tall mountain or a very long rod in space) where g changes from one part of the body to another.
When g varies across the body. If one part of the body is in a stronger gravitational field than another, the lower (stronger-g) part gets more weight, so the weight point (CG) shifts toward that part, away from the pure mass point (CM). This needs a non-uniform field, so it matters only for extremely large bodies.
No. Centre of mass depends only on how the mass is distributed (m1r1 + m2r2 ... / total mass). It has nothing to do with g. Centre of gravity DOES depend on g, because it is about weight (mg). Turn gravity off and the CM stays put, but 'centre of gravity' has no meaning.
The centre of gravity is the point about which the total gravitational torque on the body is zero. If you support the body exactly at its CG, the weights of all the tiny parts produce torques that cancel out, so the body balances. This is the definition NEET 2017 asked about directly.
It is a geometric point, not a particle. It may even lie outside the body (for example, the centre of a ring or a horseshoe). No matter is required at the CM; it is simply the balance point of the mass distribution that lets us treat the whole body as one particle.
Which of the following statements are correct? (a) The centre of mass of a body always coincides with its centre of gravity. (b) The centre of mass is the point where the total gravitational torque on the body is zero. (c) A couple on a body produces both translational and rotational motion. (d) Mechanical advantage greater than one means a small effort can lift a large load.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
At the same point. Because g is uniform over a small body, the mass point and the weight point sit on top of each other. This is why we freely say 'CG' and 'CM' interchangeably in most NEET numericals.
Yes, just like the centre of mass. For a ring, a hollow shell, or an L-shaped body, both the CM and (in a uniform field) the CG lie in empty space, not in the material of the body.
The centre of gravity. A body balances when supported at its CG, because there the total gravitational torque is zero. In a uniform field this support point is also the CM, so we usually just balance at the CM.
Yes. Both depend on how mass is arranged. Changing the shape or moving mass around moves the CM (mass distribution) and, in a uniform field, moves the CG with it.
