Which one of the following statements for second law of motion is NOT correct?
- (a)The net force on a body is proportional to that body's acceleration
- (b)The net force on a body is in the same direction as the acceleration
- (c)The time rate of change of momentum is equal to force
- (d)The net force on a body is proportional to that body's momentum
Correct — D, 'The net force on a body is proportional to that body's momentum'. This is the false statement (the question asks which is NOT correct). Newton's second law says force equals the time rate of change of momentum, F = dp/dt, which reduces to F = ma. Force is proportional to how fast momentum changes, not to the momentum itself — a fast-moving body with constant momentum has no net force on it.
- (a)The net force on a body is proportional to that body's acceleration — This is a CORRECT statement, so it is not the answer. F = ma means net force is directly proportional to acceleration (with mass as the constant of proportionality).
- (b)The net force on a body is in the same direction as the acceleration — This is a CORRECT statement. Force and acceleration are vectors linked by F = ma, so they always point in the same direction.
- (c)The time rate of change of momentum is equal to force — This is the CORRECT and most general form of the second law: F = dp/dt. It is exactly what the false option (d) distorts, so (c) is true, not the answer.
Newton's second law of motion states that the net force on a body equals the rate of change of its momentum, F = dp/dt. For constant mass this becomes F = ma, so force is proportional to acceleration and points in the same direction as it. The law defines how forces change motion.
The trap swaps 'rate of change of momentum' for 'momentum'. A body can carry huge momentum yet feel zero net force if that momentum is not changing — a train at steady speed is the classic case. Only the option that drops the words 'rate of change' is false.
- Newton's second law: net force equals the rate of change of momentum, F = dp/dt.
- For constant mass this simplifies to F = ma, so force is proportional to acceleration.
- Force and acceleration are vectors pointing in the same direction.
- A body moving at constant velocity has constant momentum and therefore zero net force, even though its momentum is large.
Only the 'proportional to momentum' claim is false, so the NOT-correct statement is (d).
- Force is tied to the RATE OF CHANGE of momentum, not to momentum itself.
- Big momentum does not mean big force — constant momentum means zero net force.
The second law is tested as 'which statement is NOT correct', hiding the error in a swap of 'rate of change of momentum' for 'momentum'.
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 conceptual root — Newton's law of motion expressed through momentum. UPSC tested that momentum changes only when an external force acts; the NDA question tests the companion idea that force equals the RATE OF CHANGE of momentum, not the momentum itself.
- practice — not a real PYQ
The most general statement of Newton's second law of motion is
- (a)F = mv
- (b)F = dp/dt
- (c)F = mgh
- (d)F = ½mv²
Answer(b) F = dp/dt — force equals the time rate of change of momentum, which gives F = ma for constant mass.
- practice — not a real PYQ
A body moving with constant velocity has
- (a)zero net force acting on it
- (b)increasing momentum
- (c)a net force in the direction of motion
- (d)zero momentum
Answer(a) zero net force acting on it — constant velocity means constant momentum, so the rate of change of momentum, and hence the net force, is zero.