Physics Fundamentals

Three short sentences, written by Isaac Newton in 1687, still explain everything from why a bus passenger jerks forward when the brakes hit, to how an ISRO rocket leaves Earth. For RPF Constable and every General Science paper, these three laws are guaranteed marks if you understand them in pictures, not formulas.

Definition: A force is a push or a pull that can change the state of motion of a body. The SI unit of force is the newton (N), where 1 N = 1 kg·m/s² — the force needed to accelerate a 1-kilogram body at 1 metre per second squared.

Definition: Inertia is the natural tendency of a body to resist any change in its state of motion or rest. The larger the mass, the larger the inertia.

First Law — the Law of Inertia

"A body continues in its state of rest or of uniform motion in a straight line unless acted upon by an external unbalanced force."

This law overturns the everyday intuition that motion needs a force to keep going. In reality, motion fades only because friction and air resistance act on it. Remove those forces — as in deep space — and a body keeps moving forever in a straight line at the same speed.

Indian everyday examples make this law instinctive:

• When a bus suddenly brakes, your body lurches forward because it was already moving with the bus, and inertia tries to keep it moving.
• When a bus suddenly accelerates, your body jerks backward because it was at rest and inertia tries to keep it at rest.
• A coin placed on a card on a glass slips into the glass when the card is flicked away — the coin's inertia keeps it at rest while the card shoots out from under it.

The first law also gives the operational definition of force: anything that can change the velocity of a body — start it, stop it, speed it up, slow it down or turn it — is a force.

Second Law — F = ma, the quantitative law

"The rate of change of momentum of a body is directly proportional to the applied force and takes place in the direction of the force."

Definition: Momentum (p) is the product of mass and velocity: p = mv. It is the "quantity of motion" carried by a body.

Mathematically the law is written as F = dp/dt. If the mass is constant, F = m (dv/dt) = m · a, giving the familiar F = ma.

This law lets us calculate. If a 1500 kg car is to accelerate at 2 m/s², we know instantly that the engine must apply 3000 N of force. If a 50 g cricket ball is bowled at 36 m/s (= 10 m/s × 3.6 ... wait, 36 km/h = 10 m/s), and a batsman returns it at the same speed in the opposite direction in 0.01 seconds, the change in momentum is m × (v_final − v_initial) = 0.05 × (10 − (−10)) = 1 kg·m/s, and the average force on the ball is 1 / 0.01 = 100 N.

The second law is also the reason a heavier vehicle needs more braking force to stop in the same distance. Trucks have larger brakes than scooters for exactly this reason.

Third Law — action and reaction

"To every action there is an equal and opposite reaction."

The crucial thing students miss: the action and the reaction act on two different bodies, never on the same one. So they do not cancel each other out.

• A gun recoils backwards when a bullet shoots forward. Action: gun pushes bullet. Reaction: bullet pushes gun.
• A rocket rises because exhaust gases shoot downward at high speed; the reaction pushes the rocket upward. This is the operating principle of every PSLV and GSLV launch from Sriharikota.
• Swimming works because you push the water backward with your hands; the water pushes you forward.
• Walking is the same idea — your foot pushes the ground backward, and the ground pushes you forward. On a frictionless surface you cannot walk, because there is nothing to push back against.

Why it matters: RPF Constable, SSC GD, NDA, CDS and almost every General Science section asks at least one direct question from Newton's laws — usually identifying which law explains a given everyday situation, or solving a one-step F = ma sum. Knowing one example per law and the SI unit of force locks the easy marks.

Real-world example: When ISRO's Chandrayaan-3 lander used its retrorockets to slow down before touching the lunar surface (August 2023), it was Newton's third law at work. The rocket nozzles fired downward; the reaction pushed the lander upward, gently decelerating it from 1.68 km/s to a soft landing. The whole descent was an exercise in repeatedly applying F = m·a in reverse.

Common misconception: "If action and reaction are equal and opposite, they cancel each other, so nothing should move." Wrong. The two forces act on different bodies — one on the bullet, one on the gun — so each body has a net force on it, and each accelerates (the bullet a lot, the gun a little, because of the mass difference).

Another classic confusion: students think the second law is only F = ma. The deeper form is F = dp/dt, which also handles changing-mass situations like a rocket burning fuel.

Question: A 5 kg block is acted on by a horizontal force of 20 N on a smooth surface. Find its acceleration.

Solution:
Step 1: Apply Newton's second law: F = m·a.
Step 2: Rearrange to a = F / m = 20 / 5 = 4 m/s².
Conclusion: The block accelerates at 4 m/s² in the direction of the applied force.

:::compare

Law	Statement (one-line)	Standard example
First (Inertia)	Body at rest stays at rest; moving body stays moving — until a force acts.	Passenger jerks forward when bus brakes.
Second (F = ma)	Force = mass × acceleration; force changes momentum.	Heavier truck needs more brake force to stop.
Third (Action–Reaction)	Every action has equal & opposite reaction on another body.	Gun recoils; rocket lifts off; you swim forward.
:::

:::keypoints

• First law = Law of Inertia; explains seat-belt and headrest design.
• Mass measures inertia — a heavier body resists motion change more.
• Second law: F = ma, deeper form F = dp/dt (rate of change of momentum).
• SI unit of force = newton (N) = 1 kg·m/s².
• Momentum p = mv; force = rate of change of momentum.
• Third law: action and reaction act on two different bodies — they never cancel.
• Rocket propulsion, swimming, walking, recoil of a gun — all third law.
• Memory aid: "1-Inertia, 2-Force, 3-Reaction".
  :::

:::memory
"I-F-R" — Inertia, Force, Reaction — first, second, third law in order. Pair it with one Indian picture each: bus jerk, truck braking, ISRO rocket. Three pictures, three laws, locked.
:::

:::recap

• First law: bodies resist change in motion — that resistance is inertia.
• Second law: F = ma; force gives quantitative meaning to push and pull.
• Third law: every action produces an equal and opposite reaction on a different body.
• SI unit of force is the newton; 1 N = 1 kg·m/s².
  :::

If you open any past UPSC Prelims paper from the last twenty years and search for "Bhakti" or "Sufi", you will find the same question pattern repeating — a match-the-following between a saint, the region where they preached, and a specific contribution (a deity, a text, an institution, a doctrine). This lesson is a quick-recall map of the most frequently asked saint–region–contribution pairings, organised so that you can revise the entire Medieval India Bhakti and Sufi syllabus in a single sitting.

Definition: The Bhakti movement was a wave of devotional religious reform, broadly from the 7th to the 17th century, that emphasised a direct, personal, emotional relationship between the devotee and a single God — without need for elaborate ritual or priestly mediation.
Definition: The Sufi movement was the mystical, inward-looking strand of Islam that emphasised love of God, music (sama), poetry, and the relationship between a teacher (pir) and disciple (murid).
Definition: A Nirguna saint worshipped a formless, attribute-less God; a Saguna saint worshipped a God with form, name and qualities — most often Rama or Krishna.

How UPSC tests this topic

Why it matters: the Bhakti–Sufi syllabus carries 2–4 Prelims questions across most years, and the marking pattern is harshly binary — either you remember the pairing or you don't. Mains GS Paper 1 also asks short-form questions on how these movements promoted social unity, syncretism, and vernacular literature. The recall table below is the single most efficient way to convert revision time into marks. Build a mental map — saint to region first, then their God or contribution — because that is exactly the order UPSC sets the option pairings.

Major Bhakti saints

Kabir (c. 1440–1518) — Varanasi / UP — Nirguna, social unity

Kabir was a weaver-poet from Varanasi (Banaras), brought up in a Muslim weaver family but a disciple of the Hindu saint Ramananda. He preached a formless, Nirguna God who could not be reached through caste, idol, mosque or temple. His sharp, witty couplets — the dohas — attacked priestly authority of both Hinduism and Islam. His verses are collected in the Bijak; some appear in the Sikh Guru Granth Sahib. UPSC angle: Kabir is the classic example of social unity Bhakti.

Guru Nanak (1469–1539) — Punjab — founded Sikhism

Born at Talwandi (Nankana Sahib) in Punjab, Guru Nanak preached one God, the brotherhood of all humans, and the equality of women. He founded the Sikh tradition; his teachings were later compiled into the Guru Granth Sahib. His successors institutionalised the langar (community kitchen) — a powerful social statement against caste.

Chaitanya (1486–1533) — Bengal — Krishna bhakti, kirtan

Chaitanya Mahaprabhu of Nadia, Bengal, was a passionate devotee of Krishna in his Radha-Krishna form. He popularised group singing of God's name — sankirtan or kirtan — and is considered, by Gaudiya Vaishnavas, a combined incarnation of Radha and Krishna. He preached in Bengal and Odisha (he settled at Puri).

Mirabai (c. 1498–1547) — Rajasthan — Krishna devotion

A Rajput princess of Mewar, Mirabai composed thousands of bhajans in Braj and Rajasthani dedicated to Krishna as her divine husband. She defied royal and caste norms and is a celebrated figure of female Bhakti agency.

Tulsidas (c. 1532–1623) — Awadh — Ramcharitmanas

Tulsidas of Awadh wrote the Ramcharitmanas — a retelling of the Ramayana in Awadhi (a dialect of Hindi) — and the Hanuman Chalisa. His Bhakti is Saguna, focused on Rama. By writing in the people's language rather than Sanskrit, he made the Rama story a household epic across North India.

Shankaradeva (1449–1568) — Assam — Vaishnavism, Sattras

In Assam, Shankaradeva founded a Vaishnav reform tradition called Ekasarana Dharma ("religion of taking refuge in one God"), with Krishna (Vishnu) as the supreme deity. He created the institution of the sattra (monastery), founded naamghar (prayer halls), wrote in Brajavali and Assamese, and developed borgeet (devotional songs) and ankiya naat (one-act plays).

Basava / Basaveshwara (12th century) — Karnataka — Lingayat / Virashaiva

A 12th-century social reformer and minister in the Kalachuri court, Basava founded the Lingayat / Virashaiva movement. His devotees worship Shiva in the form of the personal ishtalinga worn on the body. He rejected caste and the Vedic temple priesthood, and his Anubhava Mantapa ("Hall of Spiritual Experience") at Kalyana, Karnataka, was an early "parliament of saints" where men and women of all castes debated theology. His compositions are called vachanas.

Narsinh Mehta (15th century) — Gujarat

Narsinh Mehta of Junagadh, Gujarat, was a Krishna-devotee. His most famous composition is "Vaishnava Jana To" — the bhajan adopted by Mahatma Gandhi as a moral anthem and sung at his prayer meetings.

Major Sufi saints

Moinuddin Chishti (1141–1236) — Ajmer

Founder of the Chishti silsila (order) in India, Moinuddin Chishti settled at Ajmer, Rajasthan. His dargah (Ajmer Sharif) remains one of South Asia's most visited pilgrimage sites for people of all faiths. Akbar walked barefoot from Agra to Ajmer to seek his blessings.

Nizamuddin Auliya (1238–1325) — Delhi

The most famous Chishti saint of the Sultanate era, Nizamuddin Auliya lived in Delhi. He never accepted royal patronage from the Sultans. His disciples included the poet Amir Khusrau, who experimented with Persian-Hindavi verse and is credited with foundational influence on Hindustani music.

Bahauddin Zakariya (1170–1267) — Multan

Founder of the Suhrawardi silsila in India, based at Multan. Unlike the Chishtis, the Suhrawardis accepted state patronage and wealth.

Shaikh Ahmad Sirhindi (1564–1624) — Mujaddid, orthodox reformer

A Naqshbandi saint based at Sirhind, Punjab, Sirhindi is known as Mujaddid-i-Alf-i-Thani — "the renewer of the second millennium" of Islam. He stood for an orthodox, reformist Sufism that rejected the syncretism and Akbar's Din-i-Ilahi. He clashed with Jahangir, who briefly imprisoned him. He is the standard UPSC example of the "conservative" turn within Sufism.

Cross-cutting facts UPSC repeats

Three patterns recur in UPSC questions:

First, language. Almost every Bhakti saint chose to compose in the vernacular — Kabir in Hindi dohas, Mirabai in Rajasthani–Braj, Tulsidas in Awadhi, Chaitanya's followers in Bengali, Shankaradeva in Brajavali / Assamese, Basava in Kannada. This break from Sanskrit was a deliberate democratisation of religion.

Second, the Nirguna–Saguna divide. Kabir, Nanak and many of the Sant tradition were Nirguna. Chaitanya, Mirabai, Tulsidas, Shankaradeva, Narsinh Mehta were Saguna. The question "Which of the following were Nirguna saints?" turns up in some form every few years.

Third, the Sufi silsilas. The four major orders in medieval India were Chishti (most influential, based in Ajmer–Delhi), Suhrawardi (Multan, wealthier), Qadiri (Punjab) and Naqshbandi (Sirhindi). Match a saint to his silsila and you have the high-yield UPSC pattern.

Real-world example: The annual Urs at Ajmer Sharif (the death anniversary of Moinuddin Chishti) draws devotees of all faiths, including Hindus and Sikhs — a living example of the Bhakti–Sufi syncretism that the syllabus emphasises. The Indian Government every year sends a ceremonial chadar to be offered at the dargah, a tradition that continues from the Mughal era.

Common misconception: students sometimes treat Bhakti and Sufi as parallel but separate movements. UPSC repeatedly tests the intersections. Kabir was deeply influenced by Sufi ideas of divine love and used the vocabulary of both traditions. Sufi shrines like Ajmer Sharif were visited by Hindu rulers. Guru Nanak's compositions in the Guru Granth Sahib include the work of Muslim figures like Sheikh Farid. The exam expects you to know the shared ground, not just the separate stories.

A second misconception is to place every Bhakti saint in North India. The southern roots are older and just as important: the Alvars (Vaishnav, worshipping Vishnu/Krishna) and Nayanars (Shaiva, worshipping Shiva) of Tamil Nadu, 6th–9th centuries, are the original wave. Ramanuja (11th century, Sri Vaishnavism), Madhva (13th century, Dvaita), and Vallabha (15th–16th century, Pushti Marg) form the southern philosophical backbone that influenced the northern movement.

:::compare

Saint	Region	God / Tradition	Key contribution
Kabir	Varanasi / UP	Nirguna	Dohas, social unity, Bijak
Guru Nanak	Punjab	One Formless God	Founded Sikhism, langar
Chaitanya	Bengal	Krishna (Saguna)	Sankirtan / kirtan
Mirabai	Rajasthan (Mewar)	Krishna	Bhajans in Rajasthani–Braj
Tulsidas	Awadh (UP)	Rama	Ramcharitmanas, Hanuman Chalisa
Shankaradeva	Assam	Vishnu/Krishna	Ekasarana Dharma, sattras, borgeet
Basava	Karnataka	Shiva (ishtalinga)	Lingayat / Virashaiva, Anubhava Mantapa
Narsinh Mehta	Gujarat	Krishna	"Vaishnava Jana To"
Moinuddin Chishti	Ajmer	Chishti silsila	Founder in India
Nizamuddin Auliya	Delhi	Chishti silsila	Refused royal patronage; teacher of Amir Khusrau
Bahauddin Zakariya	Multan	Suhrawardi silsila	Founder; accepted state patronage
Shaikh Ahmad Sirhindi	Sirhind	Naqshbandi	Mujaddid-i-Alf-i-Thani; orthodox reform
:::

:::keypoints

• Kabir (Varanasi, Nirguna) and Guru Nanak (Punjab) emphasised one formless God and social equality.
• Chaitanya (Bengal), Mirabai (Rajasthan), Tulsidas (Awadh), Shankaradeva (Assam), Narsinh Mehta (Gujarat) were Saguna Bhakti saints centred on Krishna or Rama.
• Basava (Karnataka, 12th century) founded the Lingayat movement and the Anubhava Mantapa.
• All Bhakti saints chose vernacular languages over Sanskrit — a deliberate democratisation.
• Four main Sufi silsilas in medieval India: Chishti, Suhrawardi, Qadiri, Naqshbandi.
• Moinuddin Chishti (Ajmer) and Nizamuddin Auliya (Delhi) are the Chishti pillars.
• Shaikh Ahmad Sirhindi was the Naqshbandi reformist; rejected syncretism and Din-i-Ilahi.
• UPSC repeats the saint → region → contribution chain — map them in that order.
  :::

:::memory
"KaNa-Chai-Mi-Tul-Sha-Ba-Na" — Kabir, Nanak, Chaitanya, Mirabai, Tulsidas, Shankaradeva, Basava, Narsinh — eight Bhakti pillars in roughly the order UPSC tests them. For Sufis, "Mo-Ni-Ba-Si" — Moinuddin, Nizamuddin, Bahauddin, Sirhindi — covers nearly every saint asked.
:::

:::recap

• Lock the region first (Varanasi, Punjab, Bengal, Rajasthan, Awadh, Assam, Karnataka, Gujarat for Bhakti).
• Then the deity / tradition (Nirguna formless; Saguna Krishna or Rama).
• Then the signature contribution (text, institution, doctrine).
• For Sufis, the silsila label is the most-asked detail.
  :::

Example 1: A car at 20 m/s brakes with deceleration 5 m/s squared. Stopping distance? Using v squared = u squared + 2as with v = 0: 0 = 400 + 2(-5)s, so s = 40 m. Example 2: A bullet of mass 10 g leaves a 2 kg gun at 400 m/s. By conservation of momentum, gun recoil velocity = (0.01 x 400)/2 = 2 m/s. Tip: In recoil problems, momentum before firing is zero, so (mass of bullet x its velocity) = (mass of gun x recoil velocity). Always convert grams to kilograms before substituting.

Work is done when a force moves a body through a distance: W = Force x Displacement x cos(theta). When force and displacement are in the same direction, W = F x s. SI unit of work and energy is Joule (J); 1 J = 1 N.m. Energy is the capacity to do work. Kinetic energy (KE) = (1/2)mv squared (energy of motion). Potential energy (PE) = mgh (energy due to height). Memory aid: 'KE is for moving, PE is for position'. The Law of Conservation of Energy states energy can neither be created nor destroyed, only transformed from one form to another.

If two trucks deliver the same load to the same destination but one finishes in half the time, the faster truck has greater power — even though the work done by both is the same. Power is the physics that distinguishes a sprint from a marathon, a 1000-watt geyser from a 2000-watt geyser, and an electric scooter from a petrol motorcycle. For RPF General Science, this concept anchors at least one direct numerical every year.

Definition: Power is the rate of doing work, or equivalently the rate at which energy is transferred from one form to another. In symbols, Power = Work / Time, or P = W / t. The SI unit is the watt (W), where 1 watt equals one joule per second.

The core formula and its units

The defining formula P = W / t says nothing more than "how fast is the work being done?" If a worker lifts 100 J of grocery bags in 5 seconds, the power is 20 watts. If a hydraulic crane does the same work in 0.5 seconds, the power is 200 watts — ten times more, because the energy was delivered ten times faster.

Watt is a small unit. To talk about real machines we use larger ones:

• Kilowatt (kW) = 1000 watts. Used for room heaters, microwave ovens, electric kettles.
• Megawatt (MW) = 10^6 watts. Used for power station outputs.
• Horsepower (HP) = 746 watts approximately, or roughly 0.746 kW. Used for engines, motors, pumps.

The "approximately" matters: the value 746 W is the metric horsepower most commonly quoted in Indian textbooks. Different industries use 735.5 W (metric "PS") or 745.7 W (mechanical HP), but for RPF and NCERT, 1 HP = 746 W is the standard.

The quick-estimation trick the question setters love: HP is roughly three-quarters of a kW. So a 1 HP pump is about 0.75 kW, a 5 HP motor is about 3.75 kW. Master this in your head and you cut every HP-to-kW conversion to two seconds.

The kilowatt-hour: the commercial unit

The unit you actually pay your electricity company for is the kilowatt-hour (kWh), popularly called "one unit". It is the energy consumed by a 1 kW device running for 1 hour. Convert to joules: 1 kWh = 1000 W x 3600 s = 3.6 x 10^6 J = 3.6 MJ.

The shortcut every Class 10 NCERT chapter on electricity teaches:

Energy (kWh) = Power (kW) x Time (hours)

This single line is the basis of the electricity bill. A 1.5 kW air conditioner running for 4 hours consumes 1.5 x 4 = 6 kWh = 6 units. At Rs 8 per unit (a typical Indian tariff), that is Rs 48 per day, Rs 1440 per month. The arithmetic is small but the physics is the same as RPF questions in 2024 and 2023.

The P = F v form — power as force times velocity

There is a second, equally important formula for power: P = F v, where F is the force applied and v is the velocity in the direction of the force. To see why it is true, note that work W = Fs (force times displacement) and dividing both sides by t gives W/t = F (s/t) = F v.

This form unlocks problems where the motion is steady. A car moving at constant velocity v against a friction force F requires engine power F v just to overcome friction. A pump lifting water at a constant rate of m kilograms per second to a height h has power output (m/t) g h.

Real-world example: An Indian Railways WAP-7 electric locomotive is rated at about 6125 kW (over 8200 HP). If it pulls a passenger train at 130 km/h (about 36 m/s) against air drag and rolling resistance, the average tractive force it must overcome is roughly P/v = 6125000 / 36 ≈ 170 kN — about 17 tonnes-force. That is why goods trains hauled by the same locomotive cap out at much lower speeds: at lower v, F per unit power can be much higher, but acceleration takes longer.

Why it matters: Almost every Indian appliance is rated in watts, every engine in horsepower, every electricity bill in units. The same three relationships — P = W/t, P = Fv, and energy = P x time — explain all three. Once you internalise them, RPF Physics numericals on power become arithmetic problems with units, not physics puzzles.

Worked example — power from work and time

Question: A water pump lifts 1500 kg of water to a tank 20 m above the ground in 5 minutes. Find the power of the pump. Take g = 10 m/s^2.

Solution:

Step 1: Compute the work done against gravity. W = mgh = 1500 x 10 x 20 = 3,00,000 J.

Step 2: Convert time to SI units. t = 5 minutes = 300 s.

Step 3: Apply P = W / t = 3,00,000 / 300 = 1000 W = 1 kW.

Conclusion: The pump's output power is 1 kW, or about 1.34 HP.

Worked example — energy bill

Question: A household uses a 2 kW geyser for 1 hour daily, a 100 W bulb for 5 hours, and a 1.5 kW air conditioner for 8 hours. At Rs 8 per unit, find the daily electricity bill.

Solution:

Step 1: Compute units. Geyser: 2 x 1 = 2 kWh. Bulb: 0.1 x 5 = 0.5 kWh. AC: 1.5 x 8 = 12 kWh.

Step 2: Total = 2 + 0.5 + 12 = 14.5 units per day.

Step 3: Daily cost = 14.5 x 8 = Rs 116.

Conclusion: The daily bill is Rs 116, the monthly bill about Rs 3480.

Worked example — engine output as force-velocity

Question: A car travels at a constant speed of 72 km/h on a level road against a total resistive force of 500 N. Find the engine output power.

Solution:

Step 1: Convert 72 km/h to m/s. v = 72 x 5/18 = 20 m/s.

Step 2: Apply P = F v = 500 x 20 = 10000 W = 10 kW.

Step 3: Convert to HP if needed: 10 kW / 0.746 ≈ 13.4 HP.

Conclusion: The engine must deliver 10 kW (about 13.4 HP) at this speed.

Common misconception: Students treat "power" and "energy" as the same thing. Energy is the total fuel in the tank; power is how fast you burn it. Two devices can deliver the same energy yet differ enormously in power (think of a slow drip filling a bucket versus a fire-hose).

:::compare

Quantity	Formula	SI unit	Common unit
Work	W = Fs cos theta	joule (J)	kJ, MJ
Energy	KE = (1/2)mv^2, PE = mgh	joule (J)	kWh ("unit")
Power	P = W/t = Fv	watt (W)	kW, HP
:::

:::keypoints

• Power is the rate of doing work: P = W/t = Fv.
• SI unit watt = 1 J/s.
• 1 kW = 1000 W; 1 HP ≈ 746 W ≈ 0.746 kW.
• 1 kWh = 3.6 x 10^6 J — the commercial "unit" of electricity.
• Energy (kWh) = Power (kW) x Time (hours) — your bill in one line.
• For steady motion, P = F v lets you compute engine power directly.
• HP is roughly three-quarters of a kW — a one-second mental conversion.
  :::

:::memory
"Watt is a Joule per Second" — once you can hum that line, every unit conversion follows. For HP, remember the Indian-railway thumb rule: HP x 3 ≈ kW x 4 (since 0.746 ≈ 3/4).
:::

:::recap

• Power answers the question "how fast?" not "how much?".
• The watt, kilowatt and horsepower are simply different scales of the same unit.
• Your electricity meter measures energy in kWh — not power.
• P = Fv is the engineer's favourite form whenever speed is constant.
  :::

Example 1: A body of mass 2 kg moves at 4 m/s. KE = (1/2)(2)(4 squared) = (1/2)(2)(16) = 16 J. Example 2: An object of mass 5 kg is raised to height 10 m (g = 10). PE = mgh = 5 x 10 x 10 = 500 J. Example 3: A 100 W bulb runs for 10 hours daily for 30 days. Energy = (100/1000) kW x 10 x 30 = 30 kWh = 30 units. Tip: For KE problems square the velocity first, then multiply. For electricity, always convert watts to kilowatts by dividing by 1000.

When you hold a hot cup of chai on a cold Delhi morning, you are feeling two different physical quantities at once — the energy moving from cup to hand (heat) and the level of hotness your skin senses (temperature). RPF Constable General Science loves this distinction, and every aspirant should treat it as a guaranteed-marks topic.

Definition: Heat is a form of energy that flows from a hotter body to a colder body whenever they are in thermal contact.

Definition: Temperature is a measure of the degree of hotness or coldness of a body. It tells you how hot something is, not how much heat it contains.

Heat vs Temperature — the most-asked one-mark distinction

A small cup of tea and a large bucket of tea, both at 60 °C, are at the same temperature. But the bucket contains far more heat energy because it has many more molecules vibrating. So heat depends on mass + temperature of the body; temperature depends only on the average kinetic energy of the molecules.

This is why the SI unit of heat is the joule (J) — heat is energy. The older unit is the calorie, where 1 calorie = 4.2 J. (Mechanical equivalent of heat: J = 4.2 J/cal, established by James Prescott Joule.)

The SI unit of temperature is the kelvin (K). Other common units are degree Celsius (°C) and degree Fahrenheit (°F). The relationships you should memorise:

• 0 °C = 273 K (more precisely 273.15 K).
• 100 °C = 373 K (boiling point of water at normal atmospheric pressure).
• To convert Celsius to Kelvin: K = °C + 273.
• To convert Celsius to Fahrenheit: °F = (9/5) × °C + 32.
• −40 °C = −40 °F — the only point where the two scales coincide (a popular trick MCQ).

The three modes of heat transfer — Con-Con-Rad

Heat can travel from one place to another in three distinct ways.

1. Conduction.
Heat transfer through direct contact, mainly in solids. The molecules at the hot end vibrate more vigorously and pass their energy on to neighbouring molecules without themselves moving from their place. That is why a metal spoon dipped in hot dal soon feels hot at the handle.
Metals are good conductors (free electrons help). Wood, plastic, and air are poor conductors — which is why the wooden handle of a frying pan stays cool.

2. Convection.
Heat transfer through the bulk movement of particles in fluids (liquids and gases). Hot fluid expands, becomes less dense, and rises; cooler fluid sinks to take its place. The continuous circulation is called a convection current.
Examples: boiling water in a pot, sea breezes near a beach, the working of room heaters and refrigerators.

3. Radiation.
Heat transfer through electromagnetic waves, requiring no medium at all. The Sun's heat reaches Earth through 150 million km of empty space by radiation. Every body above absolute zero radiates infrared waves.
A black body absorbs and radiates well; a polished silver surface barely does — which is why thermos flasks have silvered inner walls (to suppress radiation).

Memory aid: Con-Con-Rad for Conduction, Convection, Radiation.

Special properties of water — favourite exam targets

Water behaves strangely between 0 °C and 4 °C — this is called anomalous expansion.

• From 0 °C to 4 °C, water actually contracts (density increases).
• Above 4 °C, it behaves normally — expands as it gets hotter.
• So water has its maximum density at 4 °C.

Why it matters in nature: in winter, the top layer of a lake cools, becomes denser at 4 °C, sinks to the bottom, while the still-colder water near the surface freezes into ice. Ice (being less dense than water) floats on top, acting as an insulating blanket. Fish and aquatic life survive winter because of this single quirk of water.

Other essentials:

• Freezing point of water = 0 °C = 273 K (at 1 atmosphere pressure).
• Boiling point of water = 100 °C = 373 K (at 1 atmosphere pressure).
• Boiling point rises with pressure (this is why pressure cookers cook dal faster — water boils at ~120 °C inside) and falls with altitude (boiling at the top of a mountain happens below 100 °C, which is why cooking takes longer at hill stations).

Real-world example — your kitchen tells you everything

A pressure cooker on a gas stove uses all three modes of heat transfer at once. The flame heats the metal base by radiation and convection of hot gases, the metal then conducts the heat to the inner contents, and the rising hot water sets up convection currents inside the cooker that cook the rajma evenly. The whistle releases steam to keep the pressure (and hence the boiling point) constant. Anomalous expansion of water explains why, on a Himachal trek in December, you can still find liquid water under a frozen lake surface.

Common misconception: Students often write that "a hotter body has more heat than a colder body." Not necessarily — a very large cold body (like an ocean at 15 °C) contains far more heat energy than a small hot body (a candle flame). Temperature is the intensity of hotness; heat is the amount of energy. Keep them separate.

Another trap: people think radiation needs air. It does not. Sunlight reaches us through the vacuum of space — radiation is the only mode of heat transfer that requires no medium.

:::compare

Property	Heat	Temperature
What it is	A form of energy in transit	Degree of hotness / coldness
SI unit	Joule (J)	Kelvin (K)
Depends on	Mass + temperature of body	Average KE of molecules
Measured by	Calorimeter	Thermometer
Two bodies same value implies?	Same total energy (if same mass)	Same hotness
:::

:::compare

Mode	Medium needed	Mainly in	Example
Conduction	Solid	Solids	Hot spoon handle
Convection	Fluid (liquid/gas)	Liquids, gases	Boiling water, sea breeze
Radiation	None (vacuum is fine)	All matter	Sun's heat, room heater glow
:::

:::keypoints

• Heat is energy (SI unit: joule); temperature is degree of hotness (SI unit: kelvin).
• 1 cal = 4.2 J (mechanical equivalent of heat).
• Three modes of heat transfer: Conduction, Convection, Radiation — Con-Con-Rad.
• Radiation needs no medium (sunlight crosses vacuum).
• Water has maximum density at 4 °C (anomalous expansion).
• 0 °C = 273 K; freezing point 0 °C, boiling point 100 °C at 1 atm.
• Boiling point rises with pressure, falls with altitude.
  :::

:::memory
"Con-Con-Rad" for the three modes (Conduction in solids, Convection in fluids, Radiation through vacuum).
"Heat is the flow; Temperature is the show." (Heat is energy in motion; temperature is the reading.)
"Four-degree water is the heaviest" — water's maximum density is at 4 °C.
:::

:::recap

• Heat = energy in joules; temperature = hotness in kelvin.
• Three modes: Conduction (solid), Convection (fluid), Radiation (no medium needed).
• Water's anomalous expansion (max density at 4 °C) keeps lake life alive.
• 0 °C = 273 K; 100 °C = 373 K at normal pressure.
  :::

Light travels in straight lines at speed about 3 x 10^8 m/s in vacuum. Reflection: angle of incidence = angle of reflection. A plane mirror forms a virtual, erect, same-size image. Concave mirror can form real or virtual images (used in torches, headlights, shaving mirrors). Convex mirror always forms a small, virtual image and gives a wide view (used as rear-view mirrors in vehicles). Refraction is bending of light when it passes between media of different densities; it causes a pencil to appear bent in water. A convex lens converges light (used for correcting hypermetropia/long-sightedness); a concave lens diverges light (used for myopia/short-sightedness). White light splits into seven colours (VIBGYOR) through a prism: dispersion.

Clap your hands. Something invisible just travelled from your palms to your ear and your brain decoded it as a sharp sound. That something is a sound wave — and RPF Constable, RRB NTPC and SSC routinely build five or six questions around what you are about to read.

Definition: Sound is a mechanical longitudinal wave produced by a vibrating body that travels through a material medium and is detected by the ear.

Two words in that definition do all the work. "Mechanical" means it needs particles to push against — a medium. "Longitudinal" means the particles of the medium vibrate back and forth in the same direction the wave is moving, creating regions of compression (squeezed-together particles) and rarefaction (spread-out particles).

Sound Needs a Medium

The classic proof is the bell-jar experiment. An electric bell is hung inside a glass jar and switched on; you can hear it ring. Now a vacuum pump slowly sucks out the air. As the air thins, the ring grows fainter until it dies away completely, even though the hammer is still visibly hitting the gong. Pump the air back in and the sound returns. Conclusion: sound cannot travel through a vacuum.

This is the single biggest difference between sound and light. Light is an electromagnetic wave and travels happily through the vacuum of space — that is why sunlight reaches us across 150 million km of empty void, while astronauts on a spacewalk must use radios to talk, not shouts.

Why it matters: Almost every General Science paper has a "sound vs light" comparison MCQ. "Which of the following can travel through vacuum?" is asked in a dozen disguises.

Speed of Sound in Different Media

In dry air at around 20 °C, sound travels at roughly 340 m/s (the textbook value is 343 m/s at 20 °C; 332 m/s at 0 °C — RPF questions accept the rounded "340 m/s"). In water, it is about 1,480 m/s, and in steel about 5,100 m/s.

The order is: solid > liquid > gas. The intuition is simple: in a solid the particles are tightly bonded — when one is pushed, it immediately shoves its neighbour. In a gas, the particles are far apart and must travel a longer distance before the push is transmitted. So denser, more rigid media carry sound faster, not slower.

Sound also speeds up as temperature rises, because hotter air molecules move faster and pass on the compression more quickly. The rough rule: +0.6 m/s for every 1 °C rise in air.

Reflection of Sound and the Echo

When sound hits a hard surface — a wall, a hill, the floor of a deep well — it bounces back. A bounced sound that you hear as a separate, repeated sound is called an echo.

Your ear can only distinguish two sounds as separate if they arrive at least 0.1 seconds (one-tenth of a second) apart. Using the speed of sound in air:

Question: What is the minimum distance from a reflecting surface for a distinct echo?

Solution:
Step 1: The sound must travel to the wall and back, so the total path = 2d.
Step 2: 2d = speed × time = 340 × 0.1 = 34 m.
Step 3: Therefore d = 17 m.
Conclusion: The reflecting surface must be at least 17 m away for a clear echo.

This 17 m is a magic number you should write on the inside of your wrist before exam day. RPF and RRB ask it directly.

The same physics gives you a reverberation — multiple overlapping echoes in a hall, which is why concert halls have curtains and corrugated ceilings to absorb stray reflections.

Pitch and Loudness

Two everyday properties of a sound — how high or how low it sounds, and how soft or loud — map onto two physical properties of the wave.

Pitch is determined by frequency (the number of vibrations per second, measured in hertz, Hz). A higher frequency means a higher pitch. A child's voice and a flute have higher pitch than a man's voice or a tabla.

Loudness is determined by amplitude (how big the to-and-fro vibration is). A bigger amplitude packs more energy into the wave, and the ear interprets that as a louder sound. Hit a drum gently and you get a soft thud; hit it hard and the same drum booms — same frequency, larger amplitude.

A third property, quality or timbre, lets you tell a sitar from a violin even when they play the same note at the same loudness; it comes from the mix of overtones in the wave.

The Audible Range and What Lies Beyond

A young, healthy human ear can hear frequencies between 20 Hz and 20,000 Hz (20 kHz) — the audible range.

• Below 20 Hz → infrasonic (or infrasound). Elephants communicate using infrasonic rumbles that travel kilometres through the ground. Earthquakes generate strong infrasonic waves.
• Above 20,000 Hz → ultrasonic (or ultrasound). Bats and dolphins navigate using ultrasonic echolocation. Humans use ultrasound for SONAR (Sound Navigation And Ranging, to map the sea bed and detect submarines), in medical imaging (pregnancy scans, gall-stone detection), in non-destructive testing of metals, in ultrasonic cleaners for jewellery, and in lithotripsy to shatter kidney stones.

As you age, the upper end of your audible range falls — many adults cannot hear above 15 kHz. This is normal, not a disease.

Real-world example: A submarine's SONAR sends out a short ultrasonic ping; some of it bounces off a hidden object and returns. By timing the round trip and using the speed of sound in seawater (~1,500 m/s), the submarine calculates the distance — exactly the echo formula above, just under the sea. This is also how fishermen in Kerala find shoals of fish with handheld fish-finders.

Common misconception: "Sound travels faster in a vacuum because there is nothing to slow it down." Completely wrong. Sound cannot travel through a vacuum at all — it needs particles to pass the disturbance along. The misconception comes from mixing up sound (mechanical wave, needs a medium) with light (electromagnetic wave, does not need a medium).

Another tripper: "Higher pitch means louder sound." No. Higher pitch means higher frequency, not greater loudness. A whisper can be high-pitched; a roar can be low-pitched.

:::compare

Property	Frequency	Amplitude
Unit	Hertz (Hz)	Metre (m) of displacement
What we perceive	Pitch (high/low note)	Loudness (soft/loud)
High value example	Whistle, baby's cry	Drum hit hard, thunder
Audible range	20 Hz – 20,000 Hz	– (varies with the source)
:::

:::keypoints

• Sound is a longitudinal mechanical wave; it must have a medium.
• Sound cannot travel through vacuum; light can — this is the classic contrast.
• Speed of sound: solid > liquid > gas; ~340 m/s in air at room temperature.
• Echo needs the reflector to be at least 17 m away (since 2d = 340 × 0.1).
• Audible range: 20 Hz to 20,000 Hz. Below = infrasonic, above = ultrasonic.
• Ultrasound is used in SONAR, foetal scans, NDT and ultrasonic cleaning.
• Pitch ↔ frequency; loudness ↔ amplitude; do not confuse them.
  :::

:::memory
"Sound needs a medium; light does not." Repeat once. Then chain it: "Solid is the fastest, gas the slowest; 17 metres is the echo line; 20 to 20,000 is the human window."
:::

:::recap

• Sound = vibration travelling through a medium; vacuum kills it.
• 340 m/s in air, faster in water, fastest in solids.
• Distinct echo needs 17 m clearance; 20 Hz–20 kHz is audible.
• Pitch comes from frequency, loudness from amplitude.
  :::

Electric current is the flow of charge; its SI unit is the Ampere (A). Ohm's Law states V = IR, where V is voltage (Volt), I is current (Ampere), and R is resistance (Ohm). Memory trick: cover the quantity you need in the V-I-R triangle. Resistances in series add up: R = R1 + R2 + ... For parallel: 1/R = 1/R1 + 1/R2 + ... Electric power P = VI = I squared R = V squared/R. SI unit of power is Watt. A good conductor (copper, silver) has low resistance; an insulator (rubber, glass) has high resistance. Fuse wire has low melting point and protects circuits from overload.

A magnet has two poles: North and South. Like poles repel, unlike poles attract. A freely suspended magnet always points North-South (used in compass). The Earth itself behaves like a giant magnet. An electric current produces a magnetic field around it (Oersted's discovery); this is the principle of the electromagnet and electric motor. A coil carrying current behaves like a bar magnet (solenoid). Magnetic substances: iron, cobalt, nickel. Memory aid for magnetic metals: 'I Co Ni' (Iron, Cobalt, Nickel). The unit of magnetic flux density is Tesla. An electric generator (dynamo) converts mechanical energy to electrical energy using electromagnetic induction.

Example 1: A 6 V battery drives a current of 2 A through a resistor. Resistance R = V/I = 6/2 = 3 Ohm. Example 2: Two resistors of 3 Ohm and 6 Ohm in series: total R = 3 + 6 = 9 Ohm. In parallel: 1/R = 1/3 + 1/6 = 3/6, so R = 2 Ohm (parallel resistance is always less than the smallest resistor). Example 3: Power of a device drawing 5 A at 220 V: P = VI = 220 x 5 = 1100 W. Tip: In series, current is the same; in parallel, voltage is the same. Always check whether the question asks for series or parallel.