Let there be an object having some chemicals in it. It starts moving with a uniform velocity v and a chemical reaction starts happening. In this case, which of the following statement/s is/are correct? 1. Chemical reactions happening in the system cannot change the velocity v of the center of mass of the object. 2. Chemical reactions happening in the system cannot change kinetic energy of the particles inside with respect to the center of mass of object. Select the correct answer using the code given below:
- (a)1 only
- (b)2 only
- (c)Both 1 and 2
- (d)Neither 1 nor 2
Correct — A, 1 only. A chemical reaction inside the object involves only internal forces, and by Newton's third law internal forces cancel in equal-and-opposite pairs, so they cannot change the total momentum or the velocity v of the centre of mass — statement 1 is true. Statement 2 is false, because a chemical reaction releases or absorbs energy (exothermic or endothermic) and that energy can change the kinetic energy of the particles measured with respect to the centre of mass, just as an internal explosion speeds its fragments up.
- (b)2 only — This reverses the truth — statement 2 is the false one (reaction energy can change internal kinetic energy), while statement 1 is correct.
- (c)Both 1 and 2 — Statement 2 is false, so both cannot be correct — internal chemical energy can raise or lower the kinetic energy of the internal particles.
- (d)Neither 1 nor 2 — Statement 1 is definitely true (internal forces cannot move the centre of mass), so 'neither' is wrong.
The centre of mass of a system moves as if all external forces acted on it alone; internal forces — including the forces of a chemical reaction — never change the system's total momentum or centre-of-mass velocity. Energy is not protected in the same way: an internal reaction can convert chemical potential energy into kinetic energy of the parts.
Keep two ideas separate — the momentum of the centre of mass, which only an external force can change, and the internal kinetic energy, which a release of chemical energy can change. The tempting error is to assume that if the centre of mass keeps gliding uniformly, nothing inside can change either.
- Internal forces occur in action-reaction pairs and cannot change a system's total momentum.
- The centre-of-mass velocity changes only under a net external force.
- Exothermic or endothermic reactions change the system's internal energy and can change its internal kinetic energy.
- A freely moving firecracker's centre of mass keeps its path even as the fragments fly apart.
Statement 1 (CM velocity fixed) is true; statement 2 (internal KE fixed) is false — so 1 only.
- Assuming uniform centre-of-mass motion means the internal energy is also fixed.
- Forgetting that a chemical reaction is a source of energy that can change internal kinetic energy.
Framed as statements about what an internal reaction changes — test each against 'momentum needs an external force' and 'energy can come from within'.
Assertion (A): A man standing on a completely frictionless surface can propel himself by whistling. Reason (R): If no external force acts on a system, its momentum cannot change.
- (a) Both A and R are true, and R is the correct explanation of A
- (b) Both A and R are true, but R is not a correct explanation of A
- (c) A is true, but R is false
- (d) A is false, but R is true
Answer(a) Both A and R are true, and R is the correct explanation of A
Same principle — internal actions cannot change a system's momentum or centre-of-mass motion; only an external force can. UPSC states it as 'no external force → momentum unchanged', which is exactly why statement 1 here is true.
- practice — not a real PYQ
A bomb at rest explodes into fragments. The velocity of the centre of mass of the fragments just after the explosion is
- (a)in the direction of the largest fragment
- (b)zero
- (c)upward
- (d)undefined
Answer(b) zero — no external force acts during the explosion, so the centre of mass stays at rest.
- practice — not a real PYQ
Internal forces within a system can change its
- (a)total momentum
- (b)centre-of-mass velocity
- (c)internal kinetic energy
- (d)none of these
Answer(c) internal kinetic energy — internal forces cannot change total momentum or CM velocity, but they can redistribute or add kinetic energy inside.