Physics Fundamentals

For uniformly accelerated motion, the three equations are: (1) v = u + at, (2) s = ut + (1/2)at^2, (3) v^2 = u^2 + 2as. Here u = initial velocity, v = final velocity, a = acceleration, t = time, s = displacement. Memory aid: 'V-U-A-S' — each equation links four of the five variables, leaving one out. Equation 1 omits s, equation 2 omits v, equation 3 omits t. For a freely falling body, a = g = 9.8 m/s^2 (often taken as 10). For a body thrown up, a = -g. SI unit of acceleration is m/s^2. These are valid ONLY when acceleration is constant.

First Law (Law of Inertia): A body stays at rest or in uniform motion unless an external force acts on it. Explains why passengers jerk forward when a bus brakes. Second Law: Force = mass x acceleration (F = ma); rate of change of momentum equals applied force. Third Law: To every action there is an equal and opposite reaction — e.g. recoil of a gun, rocket propulsion, swimming. Memory aid: 'Inertia, Force, Reaction' = 1-2-3. SI unit of force is newton (N); 1 N = 1 kg.m/s^2. The second law is the most quantitative and is the real definition of force.

A car moving at 20 m/s decelerates at 4 m/s^2. Find the distance before it stops. Using v^2 = u^2 + 2as with v = 0, u = 20, a = -4: 0 = 400 + 2(-4)s, so 8s = 400, giving s = 50 m. Shortcut for stopping distance: s = u^2 / (2a) = 400/8 = 50 m. Time to stop: v = u + at gives 0 = 20 - 4t, t = 5 s. Note: stopping distance is proportional to the SQUARE of speed — doubling speed quadruples the distance, a key road-safety fact often asked in RPF exams.

Lift a sack of grain, push a luggage trolley at a railway platform, pedal your bicycle uphill — each of these everyday actions involves the same trio of physical quantities: work, energy, and power. RPF Sub-Inspector and most General Science exams test the formulas directly, so getting them watertight pays off in seconds during the exam.

Definition: Work (W) is done on an object when a force acts on it and the object is displaced in the direction of the force (or has a component of displacement along the force).

Definition: Energy is the capacity of a body to do work. It comes in many forms (kinetic, potential, heat, light, sound, chemical, nuclear), but its SI unit is the same: the joule (J).

Definition: Power is the rate at which work is done or, equivalently, the rate at which energy is transferred or transformed.

Work — the full formula

The general formula for work done by a constant force is:

W = F × s × cos(θ)

where F is the magnitude of the applied force (in newtons), s is the magnitude of the displacement (in metres), and θ is the angle between the directions of the force and the displacement.

Three special cases drop out of this formula and each is a favourite exam question:

• If θ = 0° (force and motion in the same direction), cos 0° = 1, so W = F × s. Maximum positive work.
• If θ = 90° (force perpendicular to motion), cos 90° = 0, so W = 0. No work is done even though force is applied. A coolie carrying a suitcase horizontally on his head does zero work on the suitcase (in physics terms), because gravity is vertical but his displacement is horizontal.
• If θ = 180° (force opposite to motion), cos 180° = −1, so W = −F × s. Negative work, as in friction acting against motion.

SI unit: the joule (J), defined as 1 J = 1 N × 1 m.

CGS unit: the erg, with 1 J = 10^7 ergs.

Energy in its two mechanical forms

Two forms dominate mechanics problems:

Kinetic energy is the energy of motion. For a body of mass m moving with speed v:

KE = (1/2) m v²

Notice that KE depends on the square of speed. Doubling the speed quadruples the kinetic energy — which is precisely why braking distance grows so quickly with speed.

Potential energy stored due to height in a gravitational field, for a body of mass m raised to height h above a reference level:

PE = m × g × h

Here g ≈ 9.8 m/s² near Earth's surface (often rounded to 10 m/s² for quick mental arithmetic). The reference level can be chosen freely; only changes in PE have physical meaning.

The two are linked by the work-energy theorem: the net work done on an object equals the change in its kinetic energy. W_net = ΔKE = KE_final − KE_initial.

Power — the rate of doing work

Power = Work / Time, in symbols:

P = W / t

SI unit: the watt (W), where 1 W = 1 J/s.

For continuous force at constant velocity, there is a second highly useful form:

P = F × v

This is the formula you reach for when a question gives you a vehicle's pulling force and constant speed — or asks about the power output of a water pump lifting water at a constant rate.

A practical large unit you must know: 1 horsepower (HP) = 746 watts (sometimes rounded to 750 W in fast calculations).

The commercial unit of electrical energy

Your home electricity bill is not measured in joules — joules are too small. It is measured in kilowatt-hours (kWh), called "units":

1 unit = 1 kWh = 1000 W × 3600 s = 3.6 × 10⁶ J

So if a 1-kW electric heater runs for one hour, it consumes one unit. If a 100-W bulb glows for ten hours, that is also one unit (100 × 10 = 1000 Wh = 1 kWh).

Worked example: putting it together

Question: A pump lifts 600 kg of water to a tank 15 m above ground in 2 minutes. Assuming g = 10 m/s² and 100% efficiency, find (i) the work done and (ii) the power of the pump in watts and in HP.

Solution:

Step 1: Identify the formula for work against gravity. Lifting water at constant speed means the upward force equals the weight: F = mg. The displacement equals the height. So W = m × g × h.

Step 2: Substitute. m = 600 kg, g = 10 m/s², h = 15 m. W = 600 × 10 × 15 = 90,000 J = 90 kJ.

Step 3: Convert time to seconds. t = 2 minutes = 120 seconds.

Step 4: Apply P = W / t. P = 90,000 / 120 = 750 W.

Step 5: Convert to horsepower using 1 HP = 746 W. P = 750 / 746 ≈ 1.0 HP.

Conclusion: The pump does 90,000 joules of work and operates at about 750 W or roughly 1 horsepower.

A second quick example: kinetic energy

Question: A bullet of mass 20 g (0.02 kg) is fired at 400 m/s. What is its kinetic energy?

Solution:

Step 1: Use KE = (1/2) m v². Step 2: KE = 0.5 × 0.02 × (400)² = 0.5 × 0.02 × 160,000. Step 3: KE = 0.5 × 3200 = 1600 J.

Conclusion: A small bullet at high speed carries roughly the kinetic energy of an adult human dropped from a 2-storey balcony — which is why bullets are so destructive on impact.

Why it matters: In RPF SI, SSC, and Railway exams, work-energy-power forms a 3-to-5-marks cluster every year. Direct formula substitutions — and the units (joule, watt, kWh, HP) — are guaranteed scoring opportunities. The same content appears in NCERT Class 9 (Chapter "Work and Energy") and Class 11 Physics.

Real-world example: An Indian Railways' WAP-7 electric locomotive is rated around 6,120 kW (about 8,200 HP). If you know it pulls a load with a horizontal traction force of, say, 200 kN at 30 m/s, then power = F × v = 200,000 × 30 = 6,000,000 W = 6 MW — almost exactly the rated power. This is the P = F × v formula doing real work on real Indian tracks.

A second everyday example: A standard ceiling fan in a Tier-2 Indian city consumes about 75 W. Running it for 24 hours uses 75 × 24 = 1800 Wh = 1.8 units — explaining the bulk of a typical summer electricity bill from fans alone.

Common misconception: "If I am holding a heavy bag for ten minutes, I am doing a lot of work." In physics, no displacement = no work done on the bag, however tired you feel. (You are doing biological work inside your muscles to maintain tension, but that is internal — the physics-textbook definition only counts force × displacement on the object.)

A second confusion is between energy and power. Energy is "how much work can be done" (joules); power is "how fast it is being done" (joules per second). A small 100-W motor running all day can do more total work than a 1000-W motor running for one minute, because energy = power × time. This is exactly the logic behind the "unit" on the electricity bill.

A third trap is forgetting cos(θ) in the work formula when the force is at an angle. If a luggage trolley is pulled by a handle inclined at 60° to the ground and dragged 10 m by a force of 50 N, the work done is W = 50 × 10 × cos 60° = 250 J — not 500 J.

A fourth: students sometimes confuse horsepower (HP) with kilowatt (kW). The right relation is 1 HP = 746 W ≈ 0.746 kW. So a 100 HP car engine is roughly 74.6 kW, not 100 kW.

:::compare

Quantity	Formula	SI unit	Other units / facts
Work	W = F · s · cos θ	joule (J)	1 J = 10⁷ erg
Kinetic energy	KE = (1/2) m v²	joule (J)	Scalar; depends on v²
Gravitational PE	PE = m · g · h	joule (J)	Reference level is arbitrary
Power	P = W / t = F · v	watt (W)	1 HP = 746 W; 1 kW = 1000 W
Electrical energy (commercial)	E = P · t	kilowatt-hour (kWh)	1 unit = 1 kWh = 3.6 × 10⁶ J
:::

:::keypoints

• Work formula: W = F · s · cos θ; with force along motion it reduces to W = F · s.
• Work is zero when force is perpendicular to motion (cos 90° = 0).
• Kinetic energy depends on the square of speed: KE = (1/2) m v².
• Gravitational potential energy: PE = m · g · h.
• Power: P = W / t = F · v; SI unit is the watt.
• 1 horsepower = 746 W.
• Commercial unit of electricity: 1 kWh = 1 unit = 3.6 × 10⁶ J.
• 1 J = 1 N · m; 1 J = 10⁷ ergs.
• Work-energy theorem: net work done = change in kinetic energy.
  :::

:::memory
"WET-PoW" — pronounce it like wet-pow.

• W = Work = Force × distance (along motion)
• E = Energy stored (KE = ½mv², PE = mgh)
• T = unit is the Toule… i.e., the joule
• PoW = Power = Work ÷ time, also Force × velocity

And for the electricity bill: "Kilo, Watt, Hour — one unit" — 1 kWh = 1 unit = 3.6 × 10⁶ J.
:::

:::recap

• Work needs force, displacement, and the angle between them: W = F s cos θ.
• Kinetic energy grows with the square of speed; potential energy grows linearly with height.
• Power is the rate of doing work; the watt is its SI unit.
• The unit on your electricity bill is the kilowatt-hour, equal to 3.6 million joules.
  :::

Energy can neither be created nor destroyed; it can only be transformed from one form to another. The total energy of an isolated system remains constant. For a freely falling body, PE continuously converts to KE while total (PE + KE) stays constant. Examples: in a hydroelectric plant PE of water becomes KE then electrical energy; in a pendulum energy swings between KE (at lowest point) and PE (at extremes). Common transformations: electric bulb (electrical to light + heat), microphone (sound to electrical), solar cell (light to electrical), battery (chemical to electrical). This is one of the most frequently tested principles.

In modern IBPS PO and SBI PO cloze tests, the examiner has stopped giving you isolated blanks and started giving you paired blanks in a single sentence or one common word that must slot into three different sentences. Both formats are designed to catch the candidate who relies on "feel" instead of grammar and clause logic. This lesson walks through two fully worked examples so you can see exactly how a careful test-taker reasons.

Definition: A double-fill question gives one sentence with two blanks and asks for the pair of words that fits both. You must satisfy both blanks — a pair where one word fits but the other does not is wrong.
Definition: A common-filler question asks you to find a single word that fits naturally into three different sentences. The correct answer must be the cleanest, most idiomatic fit for all three.

Worked Example 1: Double-Fill

Question: Fill the two blanks correctly.
"The RBI sought to ___ liquidity even as it tried to ___ inflationary pressure."
Options: (a) inject / fuel (b) drain / stoke (c) inject / contain (d) absorb / spur

Solution:

Step 1: Read the sentence as one whole idea before looking at options. The Reserve Bank of India does two things at once. The connector "even as" tells you the two actions are simultaneous but the writer treats them as a deliberate balancing act.

Step 2: Lock down the second blank first, because it has stronger lexical constraints. The phrase "inflationary pressure" is a problem; the RBI fights it. So the second blank must mean "to control / reduce". Test each option's second word:

• "fuel" → fuel inflation = make it worse. Wrong direction. Eliminate (a).
• "stoke" → stoke inflation = also make it worse. Wrong direction. Eliminate (b).
• "contain" → contain inflation = control it. Correct direction. Keep (c).
• "spur" → spur inflation = push it up. Wrong direction. Eliminate (d).

After Step 2 alone, only option (c) survives.

Step 3: Verify the first blank against the surviving option. "Inject liquidity" is a standard RBI/banking phrase — it means putting more money into the financial system, usually through open-market operations or repo. Is "inject liquidity even as it tried to contain inflation" a sensible RBI move? Yes — central banks often inject short-term liquidity while still trying to anchor long-term inflation expectations. The pair is logically and stylistically right.

Conclusion: The answer is (c) inject / contain.

Notice the workflow: you did not read every option in full. You used the second blank as a filter, eliminated three options on direction alone, and only then verified the survivor. That is how you save 15–20 seconds per cloze question in IBPS PO sectional time pressure.

Worked Example 2: Common-Filler

Question: Find one common word that fits all three sentences.
(i) "Please ___ your seat."
(ii) "The shares will ___ value over time."
(iii) "They will ___ the contract tomorrow."

Solution:

Step 1: Build a small candidate list from sentence (i) alone — the most idiomatic sentence is your starting point.

• "hold your seat" — common idiom, meaning keep / retain it.
• "take your seat" — common idiom, sit down.
• "retain your seat" — possible but slightly formal.

Step 2: Apply each candidate to all three sentences. This is the step weaker candidates skip.

Test "hold":

• (i) "hold your seat" → idiomatic. ✓
• (ii) "hold value" → "shares hold their value" is standard financial English. ✓
• (iii) "hold the contract" → unusual; "hold a contract" exists but does not fit "they will hold the contract tomorrow", which suggests a future action like signing. ✗

Test "take":

• (i) "take your seat" → idiomatic. ✓
• (ii) "take value" → not idiomatic. ✗
• Eliminate.

Test "retain":

• (i) "retain your seat" → grammatical but formal.
• (ii) "retain value" → idiomatic. ✓
• (iii) "retain the contract" → could mean keep it, but not "sign / execute" it. ✗

Step 3: Recognise the trap. No single ordinary word fits all three smoothly. The setter has constructed the three sentences so that partial fits are deliberately rejected. A candidate who answers based only on the first sentence will pick "hold" and lose the mark. The setter's correct answer hinges on testing all three. In a real IBPS PO paper, if the official answer key is "sign" or "execute", sentence (iii) would have selected it; if the official key is "keep", you would have needed to confirm "keep value" and "keep the contract" both work.

Conclusion: For this prompt the cleanest common word is none of the three above — and that is the lesson. Whenever you reach a "partial fit" in a common-filler, do not commit. Re-scan the options for a verb that satisfies the strictest sentence first (here, sentence (iii)), then back-check against (i) and (ii).

Why this matters

Why it matters: in IBPS PO Prelims, the cloze section is often the fastest scoring part of English — five marks in under three minutes for a prepared candidate. But the same section becomes a trap when you treat each blank as independent. New-pattern cloze is engineered so that clause logic (semantic direction) filters out 50% of options, collocation filters another 25%, and only the remaining options need the slow verification step. Internalising this filter-first workflow saves time everywhere in Verbal Reasoning, not just in cloze.

Real-world example: in the IBPS PO Mains 2022 paper, six of the ten Reading Comprehension + Cloze marks were decided by candidates who could read the connector word ("although", "even as", "thus", "however") and infer direction before scanning options. The candidates who scanned options first ran out of time on the DI section.

Common misconception: many aspirants believe that if they "know more English vocabulary" they will automatically clear cloze. Vocabulary helps, but the real edge is clause analysis. Even with a smaller vocabulary you can score full marks if you systematically use connectors ("even as", "yet", "since", "because") to decide whether the missing word is positive or negative, cause or consequence, same direction or opposite direction. After that, almost every wrong option self-eliminates.

:::compare

Feature	Double-Fill	Common-Filler
Structure	One sentence, two blanks	One word, three different sentences
Filter strategy	Use the harder blank to eliminate options first	Use the strictest sentence to filter candidates first
Trap	One word fits, the other doesn't	Word fits 2 sentences but not the 3rd
Key skill	Reading the connector for direction	Testing collocation across multiple contexts
Time per question	25–35 seconds	30–40 seconds
:::

:::keypoints

• Always read connector words ("even as", "yet", "although") first — they decide direction before vocabulary.
• In double-fills, lock the harder blank first and use it as a filter on options.
• "Inflationary pressure" + "fight/control" verbs is a fixed positive-direction trap to memorise.
• "Inject liquidity" is a standard RBI collocation worth knowing for banking cloze.
• In common-fillers, never commit after the first sentence — test the candidate word in all sentences.
• Idiomatic collocation matters more than dictionary synonyms in cloze.
• Eliminate using direction (positive/negative) before evaluating style.
• Half a fit is a wrong fit — the IBPS setter deliberately designs partial fits to trap shortcut-takers.
  :::

:::memory
"DRY" workflow for any cloze blank — Direction (positive/negative from connector), Range (collocations / register), Yoke (does it bind cleanly to both halves of the sentence?). Run DRY before reading the options, and you will solve faster than the candidate who reads option (a) first.
:::

:::recap

• Double-fill: filter by the stricter blank first; only options that satisfy both survive.
• Common-filler: a word must fit all sentences; partial fits are wrong by design.
• Clause connectors decide direction; learn the standard ones and you skip half the work.
• Banking vocabulary like "inject liquidity", "contain inflation", "stoke prices" recurs every cycle — memorise the family.
  :::

Three common scales: Celsius (C), Fahrenheit (F), and Kelvin (K). Conversions: C/5 = (F-32)/9, and K = C + 273.15 (often 273). Water freezes at 0 C = 32 F = 273 K and boils at 100 C = 212 F = 373 K. Kelvin is the SI unit; 0 K is absolute zero, the lowest possible temperature. Memory aid: 'C-five, F-minus-32-nine'. Quick fact: -40 degrees is the same on both Celsius and Fahrenheit scales. Normal human body temperature is 37 C = 98.6 F. Always convert to Kelvin for gas-law problems.

Heat travels by three modes. Conduction: transfer through direct contact without movement of the material (mostly in solids/metals) — e.g. a metal spoon getting hot in tea. Convection: transfer by actual movement of heated fluid (liquids and gases) — e.g. sea breeze, boiling water, room heater warming air. Radiation: transfer through electromagnetic waves needing NO medium — e.g. heat from the Sun reaching Earth, warmth from a fire. Memory aid: 'Con-tact, Cur-rents, Rays' for Conduction, Convection, Radiation. Radiation is the only mode that works in vacuum, which is why Sun's heat reaches us through empty space.

Specific heat (c) is the heat needed to raise 1 kg of a substance by 1 degree C; Q = mc(delta T). Water has an unusually high specific heat (4186 J/kg.C), so it heats and cools slowly — moderating climate near seas. Latent heat is the heat absorbed or released during a change of state at constant temperature. Latent heat of fusion of ice = 334 J/g (melting); latent heat of vaporization of water = 2260 J/g (boiling). This is why steam at 100 C causes far more severe burns than boiling water at 100 C — it releases extra latent heat on condensing. Temperature stays constant during melting and boiling.

Reflection: light bounces off a surface; angle of incidence = angle of reflection. Refraction: light bends when passing between media of different densities (e.g. a pencil looking bent in water). Light bends TOWARDS the normal entering a denser medium, AWAY when entering a rarer one. Plane mirror forms a virtual, erect, same-size image (laterally inverted). Concave mirror (converging) is used in shaving mirrors, torches and headlights; convex mirror (diverging) gives a smaller, erect image and a wider field of view — used as vehicle rear-view mirrors. Memory aid: 'ConCAVE = CAVE inward = magnify; ConVEX = bulge out = wider view'.

Speed of light in vacuum = 3 x 10^8 m/s (the universe's speed limit; nothing travels faster). Light needs no medium and travels fastest in vacuum. Speed of sound in air at 20 C is about 343 m/s (commonly 330-340). Sound NEEDS a material medium — it cannot travel through vacuum, which is why space is silent. Sound travels FASTEST in solids, slower in liquids, slowest in gases (opposite of light). Memory aid: 'Light loves emptiness, Sound needs matter.' Wave equation: speed v = frequency (f) x wavelength (lambda). This relation applies to all waves.

An echo is reflected sound. To hear a distinct echo, the reflecting surface must be at least about 17 m away (so the sound takes at least 0.1 s to return). Frequency is measured in hertz (Hz). The audible range for humans is 20 Hz to 20,000 Hz. Below 20 Hz is infrasonic (e.g. produced by earthquakes, elephants); above 20,000 Hz is ultrasonic (e.g. used by bats, dolphins, and in sonography/SONAR). Pitch depends on frequency (higher frequency = higher pitch); loudness depends on amplitude. SONAR uses ultrasound to measure ocean depth and detect objects underwater.