Force and Laws of Motion PYQs – Physics, SSC & Railway

Correct Answer: Option 1 — 5 N
📖 Given
• Mass of the box, m = 10 kg
• Initial velocity, u = 5 m s⁻¹
• Final velocity, v = 15 m s⁻¹
• Time for which the force acts, t = 20 s
✍️ Formula
a = (v − u) / t and F = ma
🔢 Solution
• a = (15 − 5) / 20
• a = 10 / 20 = 0.5 m s⁻²
• F = m × a = 10 × 0.5
• F = 5 N
So a steady force of 5 newton is enough to speed the box up by 10 m s⁻¹ over 20 seconds. The same answer follows from the momentum form: F = (mv − mu)/t = (150 − 50)/20 = 5 N.
❌ Why the other options are incorrect
✗ 10 N — this is obtained by using the change in velocity (10) directly as the acceleration, forgetting to divide by the time of 20 s.
✗ 1 N — this comes from wrongly dividing again by the mass or from taking a = 0.1 m s⁻²; the correct acceleration is 0.5 m s⁻².
✗ 4 N — this comes from a slip such as using u = 7 m s⁻¹ or a wrong subtraction; the correct velocity change is 15 − 5 = 10 m s⁻¹.
📌 SSC & Railway Exam Facts
• Newton's Second Law: F = ma = (mv − mu)/t; 1 N = 1 kg m s⁻².
• Impulse = F × t = change in momentum; SI unit N s, same as kg m/s.
• Equations of motion: v = u + at, s = ut + ½at², v² = u² + 2as.
• If the force acts opposite to the motion, the acceleration is negative (retardation).
• Momentum is conserved in the absence of an external unbalanced force.

Correct Answer: Option 3 — Its state of motion remains unchanged.
Forces acting on a body are said to be balanced when their resultant (net) force is zero. The individual forces do not vanish — they simply cancel one another out.
By Newton's Second Law, F = ma, if the net force F = 0 then the acceleration a = 0. Zero acceleration means the velocity cannot change either in magnitude or in direction. So a body at rest stays at rest, and a body moving with uniform velocity keeps moving with the same speed in the same straight line. This is precisely the content of Newton's First Law of Motion.
A book lying on a table is the classic example: its weight acting downwards is exactly balanced by the normal reaction of the table acting upwards, so the book stays at rest. Balanced forces can still change the shape of a body, as when a rubber ball is squeezed from both sides.
❌ Why the other options are incorrect
✗ It speeds up. — speeding up needs a positive acceleration, which requires an unbalanced force along the direction of motion.
✗ It slows down. — slowing down is retardation, produced by an unbalanced force acting opposite to the motion, such as friction.
✗ It changes its direction of motion. — changing direction is also a change of velocity, and so needs an unbalanced force acting sideways, as in circular motion.
📌 SSC & Railway Exam Facts
• Balanced forces → net force zero → no acceleration; unbalanced forces → acceleration.
• Newton's First Law (Law of Inertia) describes exactly this situation.
• Balanced forces cannot change the state of motion but can change the shape of a body.
• Friction is an example of an unbalanced force that brings a moving body to rest.
• F = ma; SI unit of force is the newton (N), 1 N = 1 kg m/s².

Correct Answer: Option 4 — there is an equal and opposite reaction and they act on two different bodies
Newton's third law of motion states: "To every action there is an equal and opposite reaction." The two words that decide this question are equal, opposite — and the crucial rider that the action and the reaction always act on two different bodies.
That last point is what makes the law work. If the two forces acted on the same body they would cancel each other and nothing could ever be accelerated. Because they act on different bodies, each body feels only one of them. When you push a wall, the wall pushes you back; when a gun is fired, the bullet goes forward and the gun recoils backward; when a rocket throws hot gases down, the gases push the rocket up; and a swimmer pushes the water back to move forward.
❌ Why the other options are incorrect
✗ there is an equal and perpendicular reaction and they act on two different bodies — the reaction is opposite (180°) to the action, never perpendicular (90°).
✗ there is an unequal and opposite reaction and they act on the same body — wrong twice over: the reaction is exactly equal in magnitude, and the forces do not act on the same body.
✗ there is an equal and opposite reaction and they act on the same body — the classic trap. If both acted on one body, their resultant would be zero and no motion could ever begin.
📌 SSC & Railway Exam Facts
• Third law: action and reaction are equal, opposite and act on two different bodies; they never cancel.
• Conservation of linear momentum follows from the third law: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂.
• Recoil of a gun, rocket propulsion and walking are its standard examples.
• First law defines force and inertia; second law measures it, F = ma.
• Newton's laws appear in Principia Mathematica (1687).

Correct Answer: Option 3 — Inertia is proportional to mass.
Inertia is the natural tendency of a body to resist any change in its state of rest or of uniform motion in a straight line. This idea comes from Newton's first law of motion, which is therefore also called the law of inertia.
The measure of inertia is the mass of the body — the heavier a body is, the harder it is to start it moving, to stop it or to turn it. So inertia ∝ mass. A loaded truck is far more difficult to push than an empty cart, and a cricket ball is harder to stop than a table-tennis ball moving at the same speed, purely because of their larger masses.
❌ Why the other options are incorrect
✗ Inertia is inversely proportional to mass — exactly the opposite of the truth; if this were so, a feather would be harder to move than a truck.
✗ Inertia is independent of mass — wrong, because mass is the very measure of inertia; change the mass and the inertia changes with it.
✗ The data provided here is not adequate to draw any conclusion — no extra data is needed; the relation between mass and inertia is a standard result of Newton's first law.
📌 SSC & Railway Exam Facts
• Newton's first law = law of inertia; mass is the measure of inertia, SI unit kilogram (kg).
• Types: inertia of rest, inertia of motion and inertia of direction.
• Dust flying off when a carpet is beaten and a passenger lurching forward when a bus brakes are examples of inertia.
• Newton's second law: F = ma; momentum p = mv, SI unit kg m/s.
• Inertia is not a force — it is a property of matter, and it does not depend on velocity.

Correct Answer: Option 2 — force
This is exactly the statement of Newton's second law of motion. It says that the rate of change of momentum of a body is directly proportional to the applied unbalanced force, and the change takes place in the direction of that force.
If a body of mass m changes its velocity from u to v in time t, then rate of change of momentum = (mv − mu)/t = m × (v − u)/t = ma. Taking the constant of proportionality as 1 in SI units gives the familiar form F = ma. The SI unit of force, the newton (N), is defined from this very relation: 1 N = 1 kg m s⁻².
❌ Why the other options are incorrect
✗ torque — the turning (rotating) effect of a force, τ = r × F. It equals the rate of change of angular momentum, not of linear momentum.
✗ angular momentum — L = Iω, the rotational partner of linear momentum. It is a quantity of motion, not the cause of a change in momentum.
✗ moment of inertia — I, the rotational partner of mass; it measures how strongly a body resists a change in its rotational motion.
📌 SSC & Railway Exam Facts
• Momentum p = mv; SI unit kg m/s; it is a vector quantity.
• Newton's second law: F = dp/dt = ma — it gives the measure of force.
• 1 N = 1 kg m s⁻² and 1 dyne = 10⁻⁵ N.
• Impulse = F × t = change in momentum; SI unit N s.
• The first law gives the definition of force, the third law gives action–reaction pairs.

Correct Answer: Option 3 — 2 N
📖 Given
• Mass, m = 2 kg
• Initial velocity, u = 8 m/s
• Final velocity, v = 12 m/s
• Time, t = 4 s
✍️ Formula
a = (v − u)/t and F = ma
🔢 Solution
• a = (12 − 8)/4
• a = 4/4 = 1 m/s²
• F = m × a = 2 × 1
• F = 2 N
So a steady push of just 2 newton is enough to speed this 2 kg body up by 4 m/s over 4 seconds.
❌ Why the other options are incorrect
✗ 1 N — this is the acceleration (1 m/s²) copied down as the force; you still have to multiply it by the mass 2 kg.
✗ 3 N — no step of the calculation gives 3; it is a distractor placed between 2 and 4.
✗ 4 N — this is the change in velocity (12 − 8 = 4 m/s) mistaken for the force; the division by t = 4 s has been skipped.
📌 SSC & Railway Exam Facts
• F = ma = m(v − u)/t; SI unit newton (N), 1 N = 1 kg m s⁻².
• Impulse = F × t = m(v − u) = change in momentum; here impulse = 8 N s.
• Equations of motion: v = u + at, s = ut + ½at², v² = u² + 2as.
• 1 kgf = 9.8 N and 1 dyne = 10⁻⁵ N.

Correct Answer: Option 4 — law of inertia
Newton's first law of motion states that a body at rest stays at rest, and a body in uniform motion along a straight line keeps moving that way, unless an external unbalanced force acts on it. Because the law simply describes the natural tendency of matter to resist a change in its state of motion, it is called the law of inertia.
Inertia is measured by mass — the heavier the body, the greater its inertia. It appears in three forms: inertia of rest, inertia of motion and inertia of direction. Everyday proofs are a passenger falling backwards when a bus starts suddenly (inertia of rest), falling forwards when it brakes (inertia of motion), and dust flying off a carpet that is beaten.
❌ Why the other options are incorrect
✗ law of angular momentum — this is the conservation of angular momentum (L = Iω), a rotational result, not Newton's first law.
✗ law of linear momentum — conservation of linear momentum follows from Newton's third law together with the second law.
✗ law of torque — torque τ = r × F describes the turning effect of a force; there is no "first law of torque".
📌 SSC & Railway Exam Facts
• First law — defines force and inertia; Second law — measures force, F = ma; Third law — action and reaction.
• Inertia ∝ mass; SI unit of mass kilogram (kg).
• Newton's laws were published in Philosophiæ Naturalis Principia Mathematica (1687).
• Galileo gave the idea of inertia before Newton formalised it.

Correct Answer: Option 3 — 6 m/s
📖 Given
• Constant force, F = 4 N
• Mass of the box, m = 2 kg
• Time for which the force acts, t = 2 s
• Initial velocity, u = 2 m/s
• To find: final velocity, v
✍️ Formula
Newton's second law: F = ma, so a = F/m; then the first equation of motion v = u + at
🔢 Solution
• a = F/m = 4/2
• a = 2 m/s²
• v = u + at = 2 + (2 × 2)
• v = 2 + 4
• v = 6 m/s
In plain language: the 4 N force makes the box speed up by 2 m/s in every second, so in 2 s it gains 4 m/s, which added to its starting 2 m/s gives 6 m/s.
❌ Why the other options are incorrect
✗ 2 m/s — this is the initial velocity u; it would be the answer only if no force acted at all.
✗ 3 m/s — obtained by wrongly taking a = 0.5 m/s² (dividing 2 by 4 instead of 4 by 2).
✗ 4 m/s — this is only the gain in velocity (at = 4 m/s); the initial velocity of 2 m/s has been forgotten.
📌 SSC & Railway Exam Facts
• Newton's second law: F = ma = (mv − mu)/t — force equals the rate of change of momentum.
• SI unit of force is the newton (N): 1 N = 1 kg m/s², the force that gives a 1 kg mass an acceleration of 1 m/s².
• The three equations of motion: v = u + at, s = ut + ½at², v² = u² + 2as.
• Change of momentum here = m(v − u) = 2 × (6 − 2) = 8 kg m/s, which equals impulse = F × t = 4 × 2 = 8 N s.
• Newton's third law: every action has an equal and opposite reaction, acting on two different bodies.

Correct Answer: Option 3 — unbalanced force
An object starts moving, speeds up, slows down or changes direction only when the net force acting on it is not zero. Such a net force is called an unbalanced force. This is the content of Newton's first law of motion, which says a body continues in its state of rest or of uniform motion unless an unbalanced external force acts on it.
On a horizontal table the weight of the object acting downward is exactly cancelled by the normal reaction of the table acting upward. These two are balanced, so they cannot move the object sideways. To slide it, the applied push must be greater than the force of friction, leaving an unbalanced force that produces acceleration according to F = ma.
❌ Why the other options are incorrect
✗ an equal amount of perpendicular forces on the object in both upward and downward directions — equal and opposite forces cancel out; their resultant is zero and the object stays where it is.
✗ only a single force perpendicular to the object — a force perpendicular to the table presses the object down or lifts it; it does not push it along the table.
✗ balanced force — balanced forces give a zero resultant, so they can only change the shape of a body, never its state of motion.
📌 SSC & Railway Exam Facts
• Newton's first law is also called the law of inertia; it defines force.
• Newton's second law: F = ma; SI unit of force is newton (N), where 1 N = 1 kg m/s².
• Newton's third law: every action has an equal and opposite reaction.
• Friction always opposes relative motion; static friction > kinetic friction.
• Balanced forces can change the shape of an object (e.g. squeezing a rubber ball) but not its velocity.

Correct Answer: Option 4 — 20 N
📖 Given
• Mass of the box, m = 10 kg
• Initial velocity, u = 6 m/s
• Final velocity, v = 10 m/s
• Time for which the force acts, t = 2 s
✍️ Formula
a = (v − u)/t and F = ma
🔢 Solution
• a = (10 − 6)/2
• a = 4/2 = 2 m/s²
• F = m × a = 10 × 2
• F = 20 N
So a steady push of 20 newton is enough to raise the speed of this 10 kg box by 4 m/s in 2 seconds.
❌ Why the other options are incorrect
✗ 40 N — this comes from taking the acceleration as 4 m/s², i.e. using the change in velocity (4 m/s) directly and forgetting to divide by the time 2 s.
✗ 50 N — this is 10 × (10/2); the final velocity has been used in place of the change in velocity.
✗ 25 N — no correct step gives this; it appears if the acceleration is wrongly taken as 2.5 m/s², for example by dividing 10 m/s by 4 s.
📌 SSC & Railway Exam Facts
• Newton's second law: F = ma = (mv − mu)/t — force equals the rate of change of momentum.
• SI unit of force is the newton (N); 1 N = 1 kg m/s², the force that gives a 1 kg mass an acceleration of 1 m/s².
• Impulse = F × t = change in momentum (mv − mu); here impulse = 20 × 2 = 40 kg m/s.
• Newton's first law defines inertia; the third law says action and reaction are equal and opposite.
• 1 kgf = 9.8 N; 1 dyne = 10⁻⁵ N.

Correct Answer: Option 3 — backwards
This is a direct application of Newton's first law of motion, also called the law of inertia: a body at rest stays at rest and a body in motion keeps moving with the same velocity in a straight line unless an unbalanced external force acts on it.
When the bus is standing, our feet and our whole body are at rest. The moment the bus starts, the floor of the bus (and therefore our feet, which are in contact with it through friction) moves forward. The upper part of our body, however, still tends to remain at rest because of inertia of rest. As a result the feet go ahead while the upper body lags behind, and we fall backwards.
The opposite happens when a moving bus stops suddenly — the lower body stops, the upper body continues forward, and we lurch forward.
❌ Why the other options are incorrect
✗ left side — a sideways fall happens only when the bus takes a sharp turn, not while moving straight.
✗ right side — same reasoning; a straight start produces no sideways push.
✗ forward — we fall forward when a moving bus brakes suddenly (inertia of motion), which is the reverse situation.
📌 SSC & Railway Exam Facts
• Newton's first law defines force and inertia; it is also called Galileo's law of inertia.
• Inertia depends on mass — the greater the mass, the greater the inertia. Mass is a measure of inertia.
• Three kinds: inertia of rest, inertia of motion, inertia of direction.
• Dust flying off when a carpet is beaten, and a coin falling into a glass when the card below it is flicked, are examples of inertia of rest.
• Seat belts are provided in vehicles to counter the inertia of motion during sudden braking.

Correct Answer: Option 2 — Right
This is an application of Newton's first law of motion (the law of inertia) — in particular of the inertia of direction, which is the tendency of a body to keep moving along the same straight line unless an unbalanced external force changes its direction.
While the car moves straight, the passenger is also moving straight ahead with the same velocity. When the car suddenly turns left, the seat and the floor turn left with the car, but the passenger's body tries to keep going in the original straight-line direction. Relative to the turning car, therefore, the person is thrown towards the right, i.e. outwards from the curve.
The outward push the passenger feels is often called the centrifugal force, but this is only a pseudo (fictitious) force; the real force in the situation is the centripetal force provided by friction between the tyres and the road, which is what actually turns the car.
❌ Why the other options are incorrect
✗ Forward — a forward lurch happens when the car brakes suddenly (inertia of motion), not when it turns.
✗ Backward — a backward push happens when a stationary car suddenly accelerates (inertia of rest).
✗ Left — the person leans away from the direction of the turn, not into it; leaning left would need a force pushing them inward.
📌 SSC & Railway Exam Facts
• Three kinds of inertia: inertia of rest, inertia of motion and inertia of direction.
• Centripetal force F = mv²/r acts towards the centre; centrifugal force is a pseudo force in the rotating frame.
• Roads at curves are banked (raised on the outer edge) so that a component of the normal reaction supplies the centripetal force.
• A cyclist leans inward while turning to generate the necessary centripetal force.
• Mass is the measure of inertia — heavier bodies resist changes of motion more strongly.