Physics in the General Aptitude Test stays at the level of Class 9 and 10 science, asked about everyday things: a bus braking, a shaving mirror, a geyser's electricity bill. You need a handful of formulas, the standard cases of image formation, and a feel for why common things happen. This lesson covers units, motion and force, pressure, light and lenses, sound, electricity and magnetism, and heat, with worked examples, a ray diagram and the traps that cost the most marks.
Every physics question here is one of two kinds: a short calculation with one formula, or a "why does this happen" about something you have seen. For the first, write the formula, put the units right (metres, seconds, kilograms), and check that the answer's size makes sense. For the second, name the principle: inertia, pressure, refraction, latent heat.
Most wrong options come from a unit slip or from using the formula for the neighbouring quantity: weight for mass, power for energy, a speed for a distance.
The seven SI base units are the metre, kilogram, second, ampere, kelvin, mole and candela (luminous intensity). Everything else is derived.
| Quantity | Unit | Built from |
|---|---|---|
| Force | newton (N) | |
| Work and energy | joule (J) | |
| Power | watt (W) | |
| Pressure | pascal (Pa) |
A vector has size and direction (velocity, force, momentum); a scalar has size only (speed, mass, energy). A barometer measures air pressure. One nanometre is m, and a kilometre is mm.
Watch out
Some units sound like something else. A light year is a distance. The kilowatt-hour on a bill is energy, not power. From shortest to longest: astronomical unit, light year, parsec.
Speed conversion
Example 1 · A train's speed
A train runs at 72 km/h. What is this in m/s?
.
Check the direction: the m/s figure is always the smaller one.
20 m/s
Momentum is mass × velocity. A stone whirled in a circle at steady speed is accelerating, because its direction, and so its velocity, keeps changing.
Motion with uniform acceleration
Example 2 · A car speeding up
A car goes from 10 m/s to 30 m/s in 5 s at a steady rate. What is its acceleration, and how far does it go?
m/s².
Distance = average speed × time = m.
4 m/s² and 100 m
Mass is the amount of matter, in kilograms, and is the same everywhere. Weight is the pull of gravity, , in newtons. On the Moon, gravity is about one-sixth as strong, so a 60 kg astronaut still has a mass of 60 kg.
All bodies fall with the same acceleration whatever their mass, so a 1 kg and a 10 kg ball dropped together land together, if air is ignored.
Dropped from rest
A stone that lands after 3 s (g = 10 m/s²) has fallen m.
Pressure is force per area, . A sharp knife puts the same force on a smaller area, so the pressure is greater; wide tyres and camels' feet spread weight so they do not sink. A girl of weight 600 N on shoes of area 0.03 m² exerts Pa.
Watch out
Dividing the mass by six on the Moon is the commonest slip; only weight changes. And is not a height: the formula has .
For a convex lens, the image depends on where the object stands relative to F and 2F. A concave mirror follows the same pattern, with C in place of 2F.
| Object | Image | Nature | Use |
|---|---|---|---|
| Beyond 2F | Between F and 2F | Real, inverted, diminished | Camera |
| At 2F | At 2F | Real, inverted, same size | |
| Between F and 2F | Beyond 2F | Real, inverted, magnified | Projector |
| Inside F | Same side as object | Virtual, erect, magnified | Magnifying glass, shaving mirror |
A convex mirror and a concave lens always give a virtual, erect, diminished image; that wide view is why a convex mirror is a rear-view mirror. A plane mirror gives a virtual, upright, same-size image.
Lens, mirror and power
Example 3 · Where is the image?
An object is 15 cm in front of a convex lens of focal length 10 cm. Where is the image?
With and : .
So cm: real, on the far side, and twice as tall, as the table predicts for an object between F and 2F.
30 cm behind the lens
A convex lens has positive power, a concave lens negative: +2 D is a convex lens of focal length 50 cm, and −2 D a concave one. Short sight (myopia) is corrected with a concave lens.
Sound comes from vibration and needs a medium, so it cannot cross a vacuum. It is fastest in solids such as steel, slower in liquids, slowest in gases. Pitch depends on frequency; loudness on amplitude, measured in decibels. Humans hear 20 Hz to 20,000 Hz; below is infrasound (elephants, whales), above is ultrasound (bats).
Waves and echoes
Example 4 · Echo or lightning?
A clap's echo returns from a cliff after 2 s; thunder follows a flash by 3 s. With sound at 340 m/s, how far are the cliff and the lightning?
The echo goes there and back: m.
The light arrives almost at once, so the thunder travels one way: m.
340 m and 1,020 m
Watch out
The decibel scale is logarithmic: every 10 dB is ten times the intensity, so 60 dB is 100 times 40 dB, not 1.5 times. For a clear echo, sound must return after at least 0.1 s, so the wall must be at least 17 m away.
Circuits
In series the current is the same and the voltage is shared; in parallel the voltage is the same and the currents add. A parallel pair is smaller than its smallest resistor. Resistance grows with length: doubling a 4 Ω wire gives 8 Ω.
Example 5 · A mixed circuit
Two 6 Ω resistors are in parallel, and the pair is in series with a third 6 Ω resistor. What is the total resistance?
The parallel pair: Ω.
In series with 6 Ω: Ω.
9 Ω
Bills: energy in kWh = power in kW × hours. A 1,500 W geyser used 2 hours a day for 30 days uses kWh. A fuse melts and breaks the circuit when too much current flows; rubber is a good insulator.
A current creates a magnetic field (Oersted), which is how electromagnets work. A changing magnetic field makes a current (Faraday's electromagnetic induction): a generator turns motion into electricity, and a motor turns electrical energy into mechanical energy.
Temperature and heat
Body temperature, 37 °C, is 98.6 °F; 300 K is 27 °C; the two scales agree at −40. Raising 2 kg of water by 10 °C takes J.
| Effect | Why |
|---|---|
| A spoon handle gets hot | Conduction |
| The Sun's heat reaches Earth | Radiation, through empty space |
| A vacuum flask keeps tea hot | The vacuum stops conduction and convection |
| Coastal cities have milder weather | Water's high specific heat |
| Ice at 0 °C cools more than water at 0 °C | Melting absorbs latent heat |
| A matka keeps water cool | Evaporation takes heat away |
| Wool keeps us warm | Trapped air is a poor conductor |
| Gaps between rails | Room for expansion |
| Rice cooks slowly in Leh | Low pressure: water boils below 100 °C |
Motion
Light and sound
Electricity and heat
The chemistry of everyday things continues in everyday chemistry, and the body in biology, human body and health.
68 questions, grouped by type, easy to hard. Pick an answer and check it. The worked solution opens when you ask for it.
What is the SI unit of electric current?
AnswerB · Ampere
Current is measured in amperes, and the ampere is one of the seven SI base units.
The volt measures potential difference, the watt measures power, and the ohm measures resistance.
The three are linked: one watt is one volt times one ampere.
In SI units, force is measured in
AnswerB · newton
Force = mass × acceleration, so its unit is kg m/s², named the newton (N).
Worth noting
The joule is the unit of work and energy, the watt of power and the pascal of pressure.
The 'unit' on a household electricity bill, the kilowatt-hour, measures
AnswerD · energy
A kilowatt-hour is the energy used by a 1 kW appliance running for 1 hour.
Power × time = energy, so kWh is a unit of energy: 1 kWh = 36,00,000 J.
Worth noting
The kilowatt alone is power; multiplying by hours turns it into energy.
Which of these is a vector quantity, one that needs a direction as well as a size?
AnswerA · Velocity
Velocity is speed in a stated direction, such as 20 m/s towards the east.
Speed, mass and temperature have only a size, so they are scalars.
Worth noting
Speed and velocity are the pair most often confused: speed has no direction.
The SI unit of pressure is the
AnswerC · pascal
Pressure = force ÷ area, so its unit is N/m², called the pascal (Pa).
Worth noting
The atmosphere is a pressure unit too, but not the SI one; 1 atm is about 1,01,325 Pa.
A light year, used for the distances to stars, is a unit of
AnswerB · distance
A light year is the distance light travels in one year, about 9.46 × 10¹⁵ m.
Worth noting
The word 'year' tempts students to pick time, but the light year measures how far, not how long.
Which of the following is a base quantity in the SI system?
AnswerC · Luminous intensity
The SI system defines seven base quantities: length, mass, time, electric current, thermodynamic temperature, amount of substance and luminous intensity.
Luminous intensity is on that list, measured in candela.
Force, velocity and pressure are all derived: velocity is length over time, force is mass times acceleration, and pressure is force over area.
Worth noting
A quick test for a derived quantity is whether you can write its unit in terms of others — newtons, metres per second and pascals all decompose, candela does not.
A train runs at 72 km/h. What is this speed in metres per second?
AnswerB · 20 m/s
1 km/h = 1000 m ÷ 3600 s = 5⁄18 m/s.
72 × 5⁄18 = 20 m/s.
Worth noting
259.2 comes from multiplying by 3.6 instead of dividing; to go from km/h to m/s the number gets smaller.
One nanometre is equal to
AnswerC · 10⁻⁹ m
The prefix nano means one billionth, 10⁻⁹.
So 1 nm = 10⁻⁹ m. (Milli is 10⁻³, micro 10⁻⁶ and pico 10⁻¹².)
Which pair of quantities is measured in the same SI unit?
AnswerC · Work and energy
Work done = force × distance, measured in joules; energy is the capacity to do work, also in joules.
Power is in watts (J/s), pressure in pascals (N/m²) and acceleration in m/s², so the other pairs differ.
Which of these is NOT one of the seven SI base units?
AnswerA · newton
The seven base units are the metre, kilogram, second, ampere, kelvin, mole and candela.
The newton is derived from them: 1 N = 1 kg m/s².
Worth noting
The candela (luminous intensity) and the mole (amount of substance) sound unfamiliar, which is why students wrongly drop them.
Arrange these astronomical units of length from the shortest to the longest: light year, astronomical unit, parsec.
AnswerD · Astronomical unit, light year, parsec
An astronomical unit is the mean Earth–Sun distance, about 1.5 × 10¹¹ m.
A light year is about 9.46 × 10¹⁵ m, roughly 63,000 astronomical units.
A parsec is about 3.26 light years, so it is the longest.
The rate at which an object's velocity changes is called its
AnswerC · acceleration
Acceleration = change in velocity ÷ time taken, measured in m/s².
Standing passengers in a bus lurch forward when the driver brakes suddenly. This is because of
AnswerA · inertia of motion
The bus stops, but the passengers' bodies tend to keep moving forward.
This tendency of a moving body to stay in motion is inertia of motion (Newton's first law).
Worth noting
Inertia of rest is the opposite case: passengers fall backwards when a bus suddenly starts.
A rocket rises because it pushes hot gases downwards out of its engine. Which law explains the upward push on the rocket?
AnswerB · Newton's third law of motion
The rocket exerts a force on the gases (action); the gases exert an equal and opposite force on the rocket (reaction).
That is Newton's third law: to every action there is an equal and opposite reaction.
Worth noting
A rocket works even in space, where there is no air to push against, because the push is between the rocket and its own exhaust.
A sharp knife cuts vegetables more easily than a blunt one because the sharp edge
AnswerD · puts the same force on a smaller area, giving greater pressure
Pressure = force ÷ area.
A sharp edge has a very small area, so the same push gives a much larger pressure.
An astronaut has a mass of 60 kg on Earth. What is the astronaut's mass on the Moon, where gravity is about one-sixth as strong?
AnswerB · 60 kg
Mass is the amount of matter in a body; it does not depend on where the body is.
So the mass stays 60 kg. Only the weight falls to about one-sixth, from about 588 N to about 98 N.
Worth noting
10 kg divides the mass by 6, treating mass as if it were weight. 588 is the Earth weight in newtons, not a mass.
A scooter starts from rest and reaches 20 m/s in 5 s with uniform acceleration. What is its acceleration?
AnswerA · 4 m/s²
Acceleration = (final velocity − initial velocity) ÷ time.
= (20 − 0) ÷ 5 = 4 m/s².
Worth noting
20 is just the final velocity, 25 adds velocity and time, and 100 multiplies them; acceleration divides the change in velocity by the time.
What force is needed to give a 5 kg trolley an acceleration of 2 m/s²?
AnswerD · 10 N
By Newton's second law, F = m × a.
F = 5 × 2 = 10 N.
Worth noting
2.5, 3 and 7 come from dividing, subtracting or adding the two numbers instead of multiplying them.
A girl weighing 600 N stands on a floor. The soles of her shoes touch the floor over a total area of 0.03 m². What pressure does she exert on the floor?
AnswerD · 20,000 Pa
Pressure = force ÷ area = 600 ÷ 0.03.
600 ÷ 0.03 = 60,000 ÷ 3 = 20,000 Pa.
Worth noting
18 multiplies force by area. 200 and 2,000 are decimal-place slips when dividing by 0.03.
A stone is dropped from rest off a cliff and hits the ground 3 s later. Taking g = 10 m/s² and ignoring air resistance, how high is the cliff?
AnswerD · 45 m
For a fall from rest, height = ½ g t².
= ½ × 10 × 3² = 5 × 9 = 45 m.
Worth noting
30 m/s is the speed on landing (g × t), not the height. 9 is t² alone, and 15 uses t instead of t².
A 1 kg ball and a 10 kg ball are dropped together from the top of a tall tower. If air resistance is ignored, which reaches the ground first?
AnswerA · Both reach the ground together
Every falling body has the same acceleration due to gravity, g, whatever its mass.
The heavier ball feels a larger force, but it also has more inertia, and the two cancel.
With the same acceleration from the same height, they land together.
Worth noting
In real air a feather falls slower than a stone because of air resistance, not because it is lighter.
A pencil standing in a glass of water appears bent at the water's surface. This happens because of
AnswerB · refraction of light
Light travels at different speeds in air and in water, so it changes direction as it crosses the boundary between them. That bending is refraction.
The light from the submerged part of the pencil reaches the eye along a bent path, and the eye reads it as coming from a shifted position.
Reflection would bounce the light back, dispersion splits white light into colours, and diffraction is the spreading of light around an obstacle.
Worth noting
The same effect makes a pool look shallower than it is, and for the same reason: the light from the bottom bends on the way out.
An object is placed in front of a convex lens as shown. How does the size of its image compare with the object?
AnswerB · The same size
The object is exactly at 2F₁.
An object at 2F₁ gives an image at 2F₂ that is real, inverted and the same size as the object.
Worth noting
The image forms at infinity only when the object is at F₁, not at 2F₁.
A shaving mirror is a concave mirror held close to the face, as the object in the figure is placed. What image does it give?
AnswerA · Virtual, erect and enlarged, behind the mirror
The object (the face) is between F and the pole P.
Then a concave mirror gives a virtual, erect, enlarged image behind the mirror, which is why shaving and make-up mirrors are concave.
The clear daytime sky looks blue mainly because
AnswerA · air molecules scatter blue light much more than red light
Tiny air molecules scatter short wavelengths far more strongly than long ones.
Blue light, with a short wavelength, is scattered across the whole sky and reaches our eyes from every direction.
Worth noting
The same scattering makes the Sun look red at sunrise and sunset, when its light crosses more air and loses its blue.
The figure shows where an object is placed in front of a convex lens. What image does the lens form?
AnswerD · Real, inverted and diminished, between F₂ and 2F₂
The object is beyond 2F₁.
For an object beyond 2F₁, a convex lens forms a real, inverted, diminished image between F₂ and 2F₂. A camera lens works this way.
Where will the image be formed for the object placed in front of the convex lens in the figure?
AnswerC · Beyond 2F₂, on the other side of the lens
The object is between F₁ and 2F₁.
Then the image is real, inverted and magnified, and forms beyond 2F₂. A slide projector uses this arrangement.
Worth noting
Between F₂ and 2F₂ is the image position for an object beyond 2F₁; the two cases swap.
A student uses a convex lens as a magnifying glass, holding it as shown relative to the object. What kind of image does she see?
AnswerC · Virtual, erect and magnified
The object is between the lens and F₁, closer than the focal length.
Here the refracted rays spread out; traced back, they meet on the object's side, giving a virtual, erect, magnified image.
For the object placed in front of the concave mirror in the figure, where is the image formed?
AnswerB · Between C and F
The object is beyond C, the centre of curvature.
A concave mirror then forms a real, inverted, diminished image between C and F.
The figure shows a convex mirror, the kind fitted as a rear-view mirror on scooters. What kind of image does it form of the object?
AnswerD · Virtual, erect and diminished
A convex mirror always forms a virtual, erect, diminished image behind it, wherever the object is.
Because the image is small, the mirror shows a wide field of view, which is what a driver needs.
What is the power of a convex lens of focal length 50 cm?
AnswerC · +2 D
Power P = 1 ÷ f, with f in metres.
f = 50 cm = 0.5 m, so P = 1 ÷ 0.5 = +2 dioptre (D). A convex lens has positive power.
Worth noting
+0.02 D uses the focal length in centimetres; the dioptre needs metres.
The figure shows an object in front of a concave mirror. Which statement about its image is correct?
AnswerD · It is real, inverted and magnified, and forms beyond C
The object is between C and F.
With the object between C and F, the reflected rays meet beyond C, giving a real, inverted, magnified image.
Worth noting
This is the mirror twin of an object between F and 2F for a convex lens. Real images from a mirror form in front of it.
In the figure, a convex lens of focal length 10 cm has an object 15 cm in front of it. How far from the lens is the image formed?
AnswerD · 30 cm
Lens formula: 1/v − 1/u = 1/f, with u = −15 cm and f = +10 cm.
1/v = 1/10 + 1/(−15) = 3/30 − 2/30 = 1/30, so v = +30 cm.
The image is 30 cm from the lens on the other side, which fits an object between F and 2F.
Worth noting
6 cm comes from adding 1/10 and 1/15, forgetting that u is negative. 25 cm simply adds the distances.
An object 18 cm in front of the concave mirror of focal length 12 cm in the figure forms a real image. How many times as tall as the object is the image?
AnswerC · 2
Mirror formula: 1/v + 1/u = 1/f, with u = −18 cm and f = −12 cm.
1/v = −1/12 + 1/18 = −3/36 + 2/36 = −1/36, so v = −36 cm (36 cm in front of the mirror).
Magnification m = −v/u = −(−36)/(−18) = −2: the image is inverted and 2 times as tall.
Worth noting
1.5 is u ÷ f and 0.5 is the reciprocal of the right answer; magnification compares the image distance with the object distance.
Sound cannot travel through
AnswerC · a vacuum
Sound is a mechanical wave: it needs particles of a medium to pass the vibration on.
A vacuum has no particles, so sound cannot cross it. That is why astronauts on a spacewalk talk by radio.
A whistle sounds shrill and a drum sounds deep. The pitch of a sound depends on its
AnswerB · frequency
Pitch is how high or low a sound seems, and it rises with the number of vibrations per second, the frequency.
Worth noting
Amplitude decides loudness, not pitch: a drum can be loud and still deep.
What is the usual range of frequencies a young, healthy human ear can hear?
AnswerB · 20 Hz to 20,000 Hz
The audible range is about 20 Hz to 20 kHz (20,000 Hz).
Below 20 Hz is infrasound and above 20,000 Hz is ultrasound.
In which of these does sound travel fastest?
AnswerD · Steel
Sound is fastest in solids, slower in liquids and slowest in gases.
Roughly: steel about 5,000 m/s, water about 1,500 m/s, air about 340 m/s.
Worth noting
Warmer air carries sound slightly faster than cold air, but both are far slower than water or steel.
Bats fly and catch insects in the dark by sending out sounds and listening for the echoes. These sounds are
AnswerA · ultrasonic, above 20,000 Hz
Bats emit very high-frequency squeaks, beyond what humans can hear.
The echoes from obstacles and prey tell the bat where they are. This is echolocation.
Worth noting
Radio waves are electromagnetic, not sound; a bat's echo is a sound wave.
Kavya claps once near a cliff and hears the echo 2 s later. If sound travels at 340 m/s, how far away is the cliff?
AnswerB · 340 m
In 2 s the sound goes to the cliff and back: 340 × 2 = 680 m in all.
The cliff is half of that: 680 ÷ 2 = 340 m.
Worth noting
680 m forgets that the echo makes a return trip; always halve the total path.
During a storm, Irfan sees a flash of lightning and hears the thunder 3 s later. Taking the speed of sound as 340 m/s, about how far away was the lightning?
AnswerD · 1,020 m
Light arrives almost instantly, so the 3 s is the time the sound took.
Distance = 340 × 3 = 1,020 m, about 1 km.
Worth noting
510 m halves the distance as if it were an echo; thunder travels only one way. 340 m forgets to multiply by the time, and 113 m divides by it.
Elephants and whales communicate over long distances with sounds of frequency below 20 Hz. Such sounds are called
AnswerD · infrasonic sounds
Sound below the human audible range of 20 Hz is infrasonic.
Ultrasonic sound lies above 20,000 Hz.
Worth noting
Supersonic describes speed faster than sound, such as a fighter jet, not a frequency range.
A sound wave has a frequency of 500 Hz and a wavelength of 0.68 m. What is its speed?
AnswerB · 340 m/s
Wave speed = frequency × wavelength.
= 500 × 0.68 = 340 m/s.
Worth noting
735 divides frequency by wavelength. 34 and 3,400 are decimal slips; 340 m/s is also the familiar speed of sound in air.
A busy road measures 60 decibels and a quiet library 40 decibels. How does the intensity of the road noise compare with the library's?
AnswerC · About 100 times as great
The decibel scale is logarithmic: every 10 dB rise means 10 times the intensity.
A 20 dB rise is 10 × 10 = 100 times the intensity.
Worth noting
1.5 and 20 treat decibels like an ordinary scale, dividing or subtracting the readings.
What current flows through the circuit shown?
AnswerA · 1 A
In series, the resistances add: 4 + 8 = 12 Ω.
Current I = V ÷ R = 12 ÷ 12 = 1 A.
Worth noting
3 A and 1.5 A use one resistor alone; 4.5 A adds those two currents as if the resistors were in parallel.
What does the ammeter in the circuit shown read?
AnswerC · 1 A
Two equal 10 Ω resistors in parallel make 10 ÷ 2 = 5 Ω.
The ammeter is in the main line, so it reads 5 ÷ 5 = 1 A.
Worth noting
0.5 A is the current in one branch. 0.25 A treats the pair as 20 Ω in series.
A fuse protects the wiring of a house because it
AnswerC · melts and breaks the circuit when too much current flows
A fuse is a short wire of low melting point in series with the circuit.
An overload or short circuit heats it until it melts, cutting off the current before the house wiring overheats.
Worth noting
Earthing is a separate safety measure that carries leakage current from a metal body to the ground.
In the circuit shown, what is the potential difference across R3?
AnswerC · 5 V
Total resistance = 2 + 3 + 5 = 10 Ω, so the current is 10 ÷ 10 = 1 A.
The same 1 A flows through each resistor in series. V across R3 = I × R = 1 × 5 = 5 V.
Worth noting
10 V is the whole battery voltage; in series it is shared, in proportion to the resistances.
What is the equivalent resistance of the two resistors in the circuit shown?
AnswerB · 2 Ω
The resistors are in parallel: 1/R = 1/6 + 1/3 = 1/6 + 2/6 = 3/6 = 1/2.
So R = 2 Ω. A parallel combination is always smaller than its smallest resistor.
Worth noting
0.5 Ω is 1/R, forgetting to turn it over. 9 Ω adds them as if in series.
How much current does the battery supply to the circuit shown?
AnswerD · 3 A
In parallel each resistor has the full 6 V across it.
Branch currents: 6 ÷ 12 = 0.5 A, 6 ÷ 6 = 1 A, 6 ÷ 4 = 1.5 A.
The battery supplies their sum: 0.5 + 1 + 1.5 = 3 A. (Check: equivalent resistance 2 Ω, and 6 ÷ 2 = 3 A.)
Worth noting
0.5 A, 1 A and 1.5 A are the currents in single branches, not the total drawn from the battery.
How much power is used in R2 in the circuit shown?
AnswerB · 15 W
Series total = 5 + 15 = 20 Ω, so I = 20 ÷ 20 = 1 A.
Power in R2 = I² × R = 1² × 15 = 15 W.
Worth noting
26.7 W uses the full 20 V across R2 alone (20² ÷ 15); in series R2 gets only 15 V of it.
A student connects up the circuit shown. How much current passes through the ammeter?
AnswerC · 3 A
R2 and R3 (4 Ω each) in parallel make 2 Ω; with R1 in series the total is 1 + 2 = 3 Ω.
The ammeter is in the main line: I = 9 ÷ 3 = 3 A.
Worth noting
1 A adds all three resistors in series (9 Ω); 1.5 A is the current in one of the parallel branches.
What is the total resistance of the circuit shown, as seen by the battery?
AnswerB · 8 Ω
R2 and R3 in parallel: 12 × 6 ÷ (12 + 6) = 72 ÷ 18 = 4 Ω.
R1 is in series with that: 4 + 4 = 8 Ω.
Worth noting
22 Ω adds all three; 2 Ω puts all three in parallel; 13 Ω averages the parallel pair instead of combining it.
A 1,500 W geyser runs for 2 hours every day. How many units (kWh) of electricity does it use in 30 days?
AnswerC · 90 kWh
Power = 1,500 W = 1.5 kW.
Energy per day = 1.5 × 2 = 3 kWh; for 30 days = 3 × 30 = 90 kWh.
Worth noting
90,000 keeps the power in watts: that is 90,000 watt-hours, which is 90 kWh. 3 kWh is one day only.
An electric generator in a power station works on the principle of
AnswerA · electromagnetic induction
When a coil turns in a magnetic field, the changing magnetic field through it produces a current.
This is electromagnetic induction, discovered by Michael Faraday. A generator turns mechanical energy into electrical energy.
Worth noting
An electric motor does the reverse, turning electrical energy into motion.
Find the current in the 6 Ω resistor R2 of the circuit shown.
AnswerA · 1 A
R2 and R3 are in parallel: 6 × 3 ÷ (6 + 3) = 2 Ω. Adding R1 in series gives 2 + 2 = 4 Ω.
Battery current = 12 ÷ 4 = 3 A. The pair's voltage = 3 × 2 = 6 V.
Current through R2 = 6 ÷ 6 = 1 A (and 2 A through R3).
Worth noting
3 A is the total, which splits between R2 and R3; 2 A is R3's share.
In the circuit shown, which resistor turns more electrical energy into heat each second, and at what rate?
AnswerB · R1, at 36 W
In parallel both resistors have the full 12 V across them.
P = V² ÷ R: R1 gives 144 ÷ 4 = 36 W and R2 gives 144 ÷ 12 = 12 W.
So the smaller resistor, R1, uses more power.
Worth noting
In series the larger resistor uses more power (P = I²R, same I); in parallel the smaller one does (P = V²/R, same V).
Heat from the Sun reaches the Earth through the near-empty space between them by
AnswerB · radiation
Conduction and convection both need a material medium.
Radiation travels as electromagnetic waves and can cross a vacuum.
Normal human body temperature is about 37 °C. What is this on the Fahrenheit scale?
AnswerB · 98.6 °F
F = (9/5) × C + 32 = (9/5) × 37 + 32.
= 66.6 + 32 = 98.6 °F.
Worth noting
66.6 forgets to add 32. 104 °F is 40 °C, a high fever.
Water kept in an earthen pot (matka) stays cool in summer because
AnswerA · water seeping through the pores evaporates and takes heat from the pot
Water seeps out through tiny pores in the clay.
Evaporation needs latent heat, which it takes from the pot and the water inside, so they cool.
Woollen clothes keep us warm in winter mainly because
AnswerA · wool traps air, and air is a poor conductor of heat
The fibres hold many small pockets of still air.
Air conducts heat poorly, so the body's heat escapes slowly.
Worth noting
Clothes do not make heat; they slow the loss of the body's own heat.
At what temperature do the Celsius and Fahrenheit scales show the same reading?
AnswerA · −40°
F = (9/5) C + 32. Setting F = C: C = (9/5) C + 32.
−(4/5) C = 32, so C = −40. Then F = −40 as well.
Worth noting
At 0 °C the Fahrenheit reading is 32 °F, and at 40 °C it is 104 °F, so neither matches.
Rice takes longer to cook in an open pot at a hill station like Leh than in Chennai because, at a high altitude,
AnswerD · air pressure is lower, so water boils below 100 °C
The boiling point of water falls as the air pressure on it falls.
At high altitude water boils at, say, 88 °C, so the food cooks at a lower temperature and takes longer. A pressure cooker fixes this by raising the pressure.
Worth noting
Dissolved salts actually raise the boiling point slightly, which would speed cooking, not slow it.
Small gaps are left between the lengths of steel rail on a railway track in order to
AnswerC · allow the rails to expand in hot weather without bending
Solids expand when heated. A long steel rail can grow by several millimetres on a hot day.
Without gaps, the expanding rails would push on each other and buckle.
A laboratory reports a temperature of 300 K. What is this in degrees Celsius?
AnswerA · 27 °C
°C = K − 273.
300 − 273 = 27 °C, about room temperature.
Worth noting
573 adds 273 instead of subtracting; 149 wrongly uses the Fahrenheit formula.
Ice at 0 °C cools a drink more than the same mass of water at 0 °C does. Why?
AnswerB · Melting ice absorbs latent heat from the drink without getting any warmer
To melt, each gram of ice takes about 334 J from its surroundings while staying at 0 °C.
Water at 0 °C has no such store to take in; it only warms up. So ice removes much more heat from the drink.
Worth noting
The ice in the question is at 0 °C, the same as the water; the difference is the heat needed for melting.
Coastal cities such as Mumbai have milder summers and winters than inland cities such as Nagpur. The main reason is that
AnswerC · water has a high specific heat capacity, so the sea heats and cools slowly
Water needs much more heat than soil or rock to change its temperature by one degree.
So the sea stays cooler than the land in summer and warmer in winter, and sea breezes carry that moderating effect onto the coast.
Worth noting
Water is actually a poor conductor of heat; its high specific heat, not conduction, is what moderates the climate.
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