NEET Laws of Motion

NEET Study Guide: Laws of Motion

1. Opening Framing

Most students leave this chapter feeling confident—they can recite Newton’s three laws, solve F=ma problems, and draw free-body diagrams. Yet, in exams, they lose marks not because they don’t know the laws, but because they misapply them in dynamic scenarios (e.g., accelerating frames, variable mass, or systems with internal forces). The gap isn’t understanding the laws—it’s recognizing when to apply which law and how forces interact in non-intuitive setups (e.g., a block on a wedge, a pulley with friction, or a rocket ejecting mass).

2. Core Concepts

Concept 1: Newton’s First Law (Law of Inertia)
A body remains in its state of rest or uniform motion unless acted upon by an external unbalanced force.
Note: The "external" qualifier is critical—internal forces (e.g., tension in a rope between two blocks) cannot change the system’s center-of-mass motion. Students often misapply this to systems where forces appear balanced but aren’t (e.g., a car accelerating with passengers "pushed back" due to inertia, not a force).*

Concept 2: Newton’s Second Law (F = ma)
The net external force on a body equals its mass times its acceleration, where acceleration is measured in an inertial frame.
Note: The law is vectorial—students frequently treat it as scalar, ignoring direction (e.g., resolving forces along axes incorrectly in inclined plane problems). Also, a must be the acceleration of the center of mass, not necessarily of individual parts (e.g., a rotating rod’s COM may accelerate even if its ends don’t).*

Concept 3: Newton’s Third Law (Action-Reaction Pairs)
For every action force, there is an equal and opposite reaction force acting on different bodies.
Note: The forces in a pair never act on the same body—students often cancel them prematurely (e.g., in a block on a table, the normal force and weight are not a third-law pair; the pair to weight is Earth’s pull on the block, and the pair to normal force is the block’s push on the table).*

Concept 4: Pseudo Force (Fictitious Force)
An apparent force that acts on a body in a non-inertial (accelerating) frame to explain motion relative to that frame.
Note: Pseudo forces are frame-dependent—they vanish in inertial frames. Students confuse them with real forces (e.g., in a car turning left, the "outward push" is a pseudo force in the car’s frame, not a centrifugal force in the ground frame).*

Concept 5: Constraint Relations
Equations relating the accelerations of connected bodies (e.g., pulleys, wedges) due to geometric constraints.
Note: These are not derived from Newton’s laws but from the system’s geometry. Students often assume accelerations are equal (e.g., in a pulley with two masses, a₁ = -a₂ only if the string is inextensible; otherwise, the relation changes).*

3. Phase/Process Breakdown Table

Commonly Confused: Inertial vs. Non-Inertial Frames

4. Where Students Go Wrong (Mistake Taxonomy)

Mistake 1: Misidentifying Action-Reaction Pairs
Question (NEET 2018): A block of mass m is placed on a horizontal table. The action-reaction pair for the normal force exerted by the table on the block is: 1) The gravitational force on the block by Earth.
2) The gravitational force on Earth by the block.
3) The force exerted by the block on the table.
4) The force exerted by the block on Earth.

Common Wrong Answer: (1) The gravitational force on the block by Earth.
Reasoning Error: Students conflate balanced forces (normal force and weight acting on the same body) with action-reaction pairs (which must act on different bodies). They assume any two equal and opposite forces are a pair, ignoring the "different bodies" rule.
Correct Answer: (3) The force exerted by the block on the table.

Mistake 2: Applying F=ma to Non-Inertial Frames Without Pseudo Forces
Question (NEET 2020): A lift is moving upward with acceleration a. A man of mass m stands on a weighing machine in the lift. The reading of the machine is: 1) m(g + a) 2) m(g - a) 3) mg 4) ma

Common Wrong Answer: (3) mg.
Reasoning Error: Students apply F_net = ma in the lift’s frame but forget it’s non-inertial. They calculate N - mg = ma (correct in ground frame) but then assume N = mg (ignoring the lift’s acceleration). Alternatively, they treat the lift’s frame as inertial and miss the pseudo force.
Correct Answer: (1) m(g + a) (since N = m(g + a) in the ground frame).

Mistake 3: Incorrect Constraint Relations in Pulley Systems
Question (NEET 2019): Two blocks of masses m₁ and m₂ are connected by a light string over a frictionless pulley. If m₁ > m₂, the acceleration of the system is: 1) (m₁ - m₂)g / (m₁ + m₂) 2) (m₁ + m₂)g / (m₁ - m₂) 3) g 4) 0

Common Wrong Answer: (3) g.
Reasoning Error: Students assume the heavier mass falls with a = g (as if in free fall), ignoring the tension in the string. They forget that the string’s inextensibility imposes a₁ = -a₂, and the net force must account for both masses (m₁g - T = m₁a and T - m₂g = m₂a).
Correct Answer: (1) (m₁ - m₂)g / (m₁ + m₂).

5. Cross-Topic Connections

1. Newton’s Second Law → Rotational Motion
   The vector form F_net = ma generalizes to τ_net = Iα for rotation, where torque (τ) is the rotational analog of force, and angular acceleration (α) replaces linear acceleration. The moment of inertia (I) plays the role of mass.

2. Pseudo Forces → Gravitation (Apparent Weightlessness)
   In a freely falling elevator, the pseudo force F_pseudo = -mg cancels gravity, creating apparent weightlessness—the same mechanism as astronauts in orbit (where centripetal acceleration replaces linear acceleration).

3. Constraint Relations → Work-Energy Theorem
   In pulley systems, constraint relations (a₁ = -a₂) are used to derive work done by tension (W = TΔx), linking Newton’s laws to energy conservation (e.g., m₁gh₁ + m₂gh₂ = ½(m₁ + m₂)v²).

4. Newton’s Third Law → Collisions (Momentum Conservation)
   Action-reaction pairs ensure that internal forces cancel out in a system, leading to momentum conservation (ΣF_ext = 0 ⇒ Δp = 0). This is why collisions (even inelastic ones) conserve momentum but not kinetic energy.

6. Past Year Questions — Pattern Recognition

PYQ 1 (NEET 2021):
A block of mass m is placed on a smooth inclined plane of angle θ with the horizontal. The acceleration of the block down the plane is: 1) g sinθ 2) g cosθ 3) g tanθ 4) g

Hint Note: What’s tested: Application of F_net = ma in a non-horizontal system. The trap is assuming a = g (free fall) or misresolving forces along the wrong axis. Students who get it right know to: - Draw the free-body diagram with mg and normal force N.
- Resolve mg along the plane (mg sinθ) and perpendicular to it (mg cosθ).
- Recognize N = mg cosθ (no perpendicular acceleration) and F_net = mg sinθ = ma.

PYQ 2 (NEET 2017):
A rocket of mass M ejects mass at a rate dm/dt with exhaust velocity v relative to the rocket. The acceleration of the rocket is: 1) v (dm/dt) / M 2) v (dm/dt) / (M - dm) 3) v (dm/dt) / (M + dm) 4) v / (dm/dt)

Hint Note: What’s tested: Variable mass systems and Newton’s second law in the form F_ext = dp/dt. The trap is treating M as constant or misapplying F = ma directly. Students who get it right know: - The thrust force is v (dm/dt) (momentum flux).
- The rocket’s mass decreases over time (M(t) = M₀ - (dm/dt)t).
- The correct equation is v (dm/dt) = M(t) a (ignoring gravity for simplicity).

PYQ 3 (NEET 2016):
A block of mass m is pulled by a force F at an angle θ to the horizontal. The acceleration of the block is: 1) F cosθ / m 2) F / m 3) (F cosθ - μmg) / m 4) (F cosθ - μ(mg - F sinθ)) / m

Hint Note: What’s tested: Resolving forces and accounting for friction. The trap is ignoring the vertical component of F (which affects normal force and thus friction) or assuming a = F/m regardless of angle. Students who get it right: - Resolve F into F cosθ (horizontal) and F sinθ (vertical).
- Calculate normal force N = mg - F sinθ (reduced by vertical component).
- Use F_net = F cosθ - μN = ma.