Newton's Laws — Set 4

Correct Answer: B. It must accelerate

• **It must accelerate** = Newton's Second Law: F_net = ma; if F_net ≠ 0, then a ≠ 0 and the body accelerates. • **nonzero F_net → nonzero a** — the direction of acceleration is in the direction of the net force. • 💡 Wrong-option analysis: It stays at rest: staying at rest requires zero net force; It moves with uniform velocity: uniform velocity also requires zero net force; Its mass changes: mass is intrinsic and does not change due to a force (in classical mechanics).

Correct Answer: B. Force × Time

• **Force × Time** = Impulse J = F × Δt; it equals the change in momentum Δp = mΔv. • **J = FΔt = Δp** — large force for short time or small force for long time can give the same impulse. • 💡 Wrong-option analysis: Mass × Acceleration: this is force (F = ma), not impulse; Mass / Velocity: this has no standard physical meaning; Force / Area: this is pressure (P = F/A), not impulse.

Correct Answer: B. Inertia of Rest

• **Inertia of Rest** = When the carpet is beaten, it suddenly moves, but the dust particles tend to stay at rest due to inertia of rest and therefore fall off. • **Newton's First Law** — the dust, having no net force, remains stationary while the carpet moves away. • 💡 Wrong-option analysis: Friction: friction would keep dust on the carpet — the mechanism here is the opposite (inertia overcomes friction); Inertia of Motion: inertia of motion applies to a moving body — the dust is initially at rest; Force of Gravity: gravity acts downward continuously — it does not explain why dust detaches when the carpet is beaten.

Correct Answer: A. Both fall at the same rate

• **Both fall at the same rate** = In the absence of air resistance (vacuum), all objects experience only gravity; since g is independent of mass, all objects fall with the same acceleration g. • **g = 9.8 m/s² for all masses** — Galileo's famous experiment showed this; confirmed by the Apollo 15 feather-hammer drop on the Moon. • 💡 Wrong-option analysis: Feather: a feather falls slower only because of air resistance, which is absent here; Hammer: the hammer does not fall faster in a vacuum — both fall identically; Depends on the height: the acceleration g is constant near Earth's surface and does not depend on drop height.

Correct Answer: A. kg m/s

• **kg m/s** = Momentum p = mv; its unit is [kg] × [m/s] = kg·m/s. • **SI unit: kg·m/s** — equivalent to N·s (Newton-second), since 1 N = 1 kg·m/s². • 💡 Wrong-option analysis: N/s: this would be rate of change of force — not a standard unit; kg m/s²: this is the unit of force (Newton), not momentum; Joule-second: J·s is the unit of action (angular momentum × time), not linear momentum.

Correct Answer: B. Second Law

• **Second Law** = The Second Law F = ma is considered the 'Real Law' because it is quantitative and the First and Third Laws can be derived as special cases. • **F = dp/dt** — First Law: when F = 0, p = constant (F = 0 is a special case); Third Law follows from conservation of momentum. • 💡 Wrong-option analysis: First Law: the first law is a special case of the second (F = 0); Third Law: the third law follows from conservation of momentum, which is based on the second law; None of these: the second law is indeed considered the primary quantitative law.

Correct Answer: A. Zero

• **Zero** = Constant speed in a straight line means no change in velocity (magnitude or direction), so acceleration = 0, and by F = ma, net force = 0. • **a = 0 → F_net = 0** — this is Newton's First Law applied to a moving body. • 💡 Wrong-option analysis: Increasing: if net force were increasing, acceleration would be increasing too — inconsistent with constant speed; Constant and non-zero: a nonzero constant force would produce constant nonzero acceleration and increasing speed; Decreasing: a decreasing force means the body is slowing down — inconsistent with constant speed.

Correct Answer: A. Third Law

• **Third Law** = A jet engine expels exhaust gases backward at high speed (action); the equal and opposite reaction force pushes the aircraft forward. • **action–reaction** — the expelled gas provides thrust; this is why jet engines (and rockets) work even in the absence of a surface to push against. • 💡 Wrong-option analysis: First Law: this explains inertia — not the thrust mechanism; Pascal's Principle: relates to pressure in confined fluids — unrelated to jet propulsion; Second Law: gives F = ma for the aircraft's acceleration but does not explain why thrust is generated.

Correct Answer: C. First Law

• **First Law** = Without a seat belt, a passenger's body tends to continue moving forward at the original speed when the car suddenly stops — Newton's First Law (inertia of motion). • **inertia of motion** — the seat belt provides the external force to decelerate the passenger along with the car. • 💡 Wrong-option analysis: Second Law: while the second law describes the force needed, the reason for using seat belts is specifically inertia — the First Law; Law of Gravitation: gravity pulls downward — it does not cause forward motion during a crash; Third Law: third law is about action-reaction pairs, not about inertia.

Correct Answer: B. F ∝ a

• **F ∝ a** = Newton's Second Law: F = ma; for constant mass, F is directly proportional to a. • **F = ma → F ∝ a** — doubling force doubles acceleration; tripling force triples acceleration. • 💡 Wrong-option analysis: F ∝ a²: wrong — this would mean quadrupling force quadruples a only if a = √F, which is not the second law; F ∝ 1/a: this would mean force is inversely proportional to acceleration — the opposite of F = ma; F is independent of a: this contradicts Newton's Second Law entirely.