Sound — Waves, Shrillness, Amplitude
Q051HardBPSC Prelims
Which of the following is a correct application of ultrasound in medicine?
AX-ray imaging of bones
BSonography to image internal organs and foetus
CLaser surgery of the eye
DMRI scanning using magnetic fields
Show Answer
✔ B — Sonography to image internal organs and foetus
Ultrasound (sonography): uses high-frequency sound waves (1–20 MHz) to image soft tissues, organs, and foetus. The probe emits ultrasound; reflected waves are converted to images. Safe (no radiation), non-invasive.
*Why A is wrong:* X-rays are electromagnetic radiation, not sound waves.
*Why C is wrong:* Laser surgery uses light energy (electromagnetic), not sound.
*Why D is wrong:* MRI uses magnetic fields and radio waves, not sound.
*Why A is wrong:* X-rays are electromagnetic radiation, not sound waves.
*Why C is wrong:* Laser surgery uses light energy (electromagnetic), not sound.
*Why D is wrong:* MRI uses magnetic fields and radio waves, not sound.
Heat — Conduction, Convection, Radiation
Q052EasyBPSC Prelims
Heat transfer through direct contact between molecules (without bulk movement of matter) is called:
AConvection
BRadiation
CConduction
DEmission
Show Answer
✔ C — Conduction
- Conduction: heat transfers through molecule-to-molecule collision without bulk movement. Best in solids (metals). Example: iron rod heated at one end becomes hot throughout.
- Convection: heat transfer by actual movement of fluid (liquid/gas). Example: room heater warming air.
- Radiation: heat transfer without any medium — electromagnetic waves. Example: sunlight heating Earth.
*Why A is wrong:* Convection requires bulk movement of fluid.
*Why B is wrong:* Radiation requires no medium and works even in vacuum.
*Why D is wrong:* Emission is a general term (not a defined mode of heat transfer).
- Convection: heat transfer by actual movement of fluid (liquid/gas). Example: room heater warming air.
- Radiation: heat transfer without any medium — electromagnetic waves. Example: sunlight heating Earth.
*Why A is wrong:* Convection requires bulk movement of fluid.
*Why B is wrong:* Radiation requires no medium and works even in vacuum.
*Why D is wrong:* Emission is a general term (not a defined mode of heat transfer).
Q053EasyBPSC Prelims
The bottom of cooking vessels is made black and rough because:
ABlack surfaces are bad absorbers and good radiators
BBlack surfaces are good absorbers and good radiators
CBlack surfaces are bad absorbers and bad radiators
DColour has no effect on heat absorption
Show Answer
✔ B — Black surfaces are good absorbers and good radiators
Black surfaces (dark, rough):
- Good absorbers of heat radiation (absorb maximum heat from flame)
- Good radiators of heat (emit heat efficiently to cook food)
White/shiny surfaces are poor absorbers (reflect heat) and poor radiators. This is why solar panels are black and thermos flasks are silver-coated inside.
*Why A is wrong:* Black surfaces are GOOD absorbers (not bad).
*Why C is wrong:* Black surfaces are good at BOTH absorbing and radiating.
*Why D is wrong:* Colour/surface finish significantly affects absorption/emission (Stefan-Boltzmann law applies to blackbody radiation).
- Good absorbers of heat radiation (absorb maximum heat from flame)
- Good radiators of heat (emit heat efficiently to cook food)
White/shiny surfaces are poor absorbers (reflect heat) and poor radiators. This is why solar panels are black and thermos flasks are silver-coated inside.
*Why A is wrong:* Black surfaces are GOOD absorbers (not bad).
*Why C is wrong:* Black surfaces are good at BOTH absorbing and radiating.
*Why D is wrong:* Colour/surface finish significantly affects absorption/emission (Stefan-Boltzmann law applies to blackbody radiation).
Q054MediumBPSC Prelims
The specific heat capacity of water is 4200 J/(kg·K). What does this mean?
AWater requires 4200 J to raise its temperature by 1°C
B1 kg of water requires 4200 J to raise its temperature by 1°C
C4200 kg of water is required to produce 1 J of heat
DWater contains 4200 J of thermal energy per kg
Show Answer
✔ B — 1 kg of water requires 4200 J to raise its temperature by 1°C
Specific heat capacity (c) = amount of heat energy required to raise the temperature of 1 kg of a substance by 1°C (or 1 K).
For water: c = 4200 J/(kg·K) means 1 kg of water needs 4200 J to rise by 1°C.
*Why A is wrong:* Fails to specify "1 kg" — could be any mass.
*Why C is wrong:* This is a nonsensical restatement — the unit is J/(kg·K), not kg/J.
*Why D is wrong:* "Contains 4200 J" is about thermal energy, not the definition of specific heat capacity.
For water: c = 4200 J/(kg·K) means 1 kg of water needs 4200 J to rise by 1°C.
*Why A is wrong:* Fails to specify "1 kg" — could be any mass.
*Why C is wrong:* This is a nonsensical restatement — the unit is J/(kg·K), not kg/J.
*Why D is wrong:* "Contains 4200 J" is about thermal energy, not the definition of specific heat capacity.
Q055MediumBPSC Prelims
A bimetallic strip is used in thermostats. It works because:
ABoth metals have the same coefficient of thermal expansion
BThe two metals expand at different rates, causing bending
COne metal conducts heat faster than the other
DIt converts heat energy directly into electrical energy
Show Answer
✔ B — The two metals expand at different rates, causing bending
A bimetallic strip is made of two metals (e.g., brass and iron) bonded together. When heated:
- Brass expands more than iron (different coefficients of thermal expansion)
- The strip bends toward the metal that expands LESS (iron side)
- This bending makes or breaks an electrical circuit → thermostat action
*Why A is wrong:* If both expanded equally, there would be no bending — it would be useless as a thermostat.
*Why C is wrong:* Thermal conductivity (heat conduction speed) is irrelevant here — it's the expansion difference that matters.
*Why D is wrong:* Direct heat-to-electricity conversion describes thermocouples or thermoelectric generators, not bimetallic strips.
- Brass expands more than iron (different coefficients of thermal expansion)
- The strip bends toward the metal that expands LESS (iron side)
- This bending makes or breaks an electrical circuit → thermostat action
*Why A is wrong:* If both expanded equally, there would be no bending — it would be useless as a thermostat.
*Why C is wrong:* Thermal conductivity (heat conduction speed) is irrelevant here — it's the expansion difference that matters.
*Why D is wrong:* Direct heat-to-electricity conversion describes thermocouples or thermoelectric generators, not bimetallic strips.
Q056MediumBPSC Prelims
During the change of state from solid to liquid (melting), the temperature:
AIncreases steadily
BDecreases because energy is absorbed
CRemains constant while heat is being absorbed (latent heat)
DFirst increases then decreases
Show Answer
✔ C — Remains constant while heat is being absorbed (latent heat)
During a change of state, the heat supplied is used to break intermolecular bonds — not to raise temperature. This heat is called latent heat. Temperature remains constant until the entire substance changes state.
For ice melting to water at 0°C: temperature stays 0°C throughout melting, even as heat is continuously added.
*Why A is wrong:* Temperature doesn't increase during melting — that happens before (solid warming) or after (liquid warming).
*Why B is wrong:* Temperature doesn't decrease — it remains constant while heat is ABSORBED (endothermic process).
*Why D is wrong:* No increase-then-decrease pattern during simple state change.
For ice melting to water at 0°C: temperature stays 0°C throughout melting, even as heat is continuously added.
*Why A is wrong:* Temperature doesn't increase during melting — that happens before (solid warming) or after (liquid warming).
*Why B is wrong:* Temperature doesn't decrease — it remains constant while heat is ABSORBED (endothermic process).
*Why D is wrong:* No increase-then-decrease pattern during simple state change.
Q057HardBPSC Prelims
How much heat is needed to convert 2 kg of ice at 0°C to water at 0°C? (Latent heat of fusion of ice = 336,000 J/kg)
A168,000 J
B336,000 J
C672,000 J
D1,680 J
Show Answer
✔ C — 672,000 J
Q = m × L = 2 kg × 336,000 J/kg = 672,000 J (672 kJ)
*Why A is wrong:* 168,000 = L/2 = 336,000/2 — divided mass by 2 instead of multiplying.
*Why B is wrong:* 336,000 = L for 1 kg only; here m = 2 kg.
*Why D is wrong:* 1,680 = 336,000/200 — arithmetic error.
*Why A is wrong:* 168,000 = L/2 = 336,000/2 — divided mass by 2 instead of multiplying.
*Why B is wrong:* 336,000 = L for 1 kg only; here m = 2 kg.
*Why D is wrong:* 1,680 = 336,000/200 — arithmetic error.
Q058HardBPSC Prelims
Which of the following correctly describes the Second Law of Thermodynamics?
AEnergy can neither be created nor destroyed
BHeat spontaneously flows from a hot body to a cold body, never the reverse
CThe internal energy of an ideal gas depends only on its temperature
DThe entropy of a perfectly ordered crystal is zero at absolute zero
Show Answer
✔ B — Heat spontaneously flows from a hot body to a cold body, never the reverse
Second Law of Thermodynamics: Heat flows spontaneously from higher temperature to lower temperature — never in reverse without doing external work.
This explains why refrigerators need electricity (external work) to pump heat from cold interior to warm exterior.
*Why A is wrong:* This is the First Law (Law of Conservation of Energy).
*Why C is wrong:* This is related to the ideal gas model / Joule's experiment — not the Second Law.
*Why D is wrong:* This is the Third Law of Thermodynamics (Nernst's theorem).
This explains why refrigerators need electricity (external work) to pump heat from cold interior to warm exterior.
*Why A is wrong:* This is the First Law (Law of Conservation of Energy).
*Why C is wrong:* This is related to the ideal gas model / Joule's experiment — not the Second Law.
*Why D is wrong:* This is the Third Law of Thermodynamics (Nernst's theorem).
Electricity — Current, Resistance, Power
Q059EasyBPSC Prelims
Electric current is defined as:
AThe flow of protons through a conductor
BThe rate of flow of electric charge through a cross-section
CThe potential difference between two points
DThe resistance offered by a conductor to the flow of charge
Show Answer
✔ B — The rate of flow of electric charge through a cross-section
Electric current I = Q/t (charge Q flowing through a cross-section per unit time t)
SI unit: Ampere (A) = Coulomb per second (C/s)
In metals, current flows due to movement of free electrons (negative charges), but by convention, current direction is opposite to electron flow (from + to −).
*Why A is wrong:* Protons don't flow in solid conductors — they are fixed in the lattice. Electron flow ≠ proton flow.
*Why C is wrong:* Potential difference (voltage) is the "push" driving current, not the current itself. V = W/Q.
*Why D is wrong:* Resistance is the opposition to current flow (Ohm's law: R = V/I).
SI unit: Ampere (A) = Coulomb per second (C/s)
In metals, current flows due to movement of free electrons (negative charges), but by convention, current direction is opposite to electron flow (from + to −).
*Why A is wrong:* Protons don't flow in solid conductors — they are fixed in the lattice. Electron flow ≠ proton flow.
*Why C is wrong:* Potential difference (voltage) is the "push" driving current, not the current itself. V = W/Q.
*Why D is wrong:* Resistance is the opposition to current flow (Ohm's law: R = V/I).
Q060MediumBPSC Prelims
A conductor of resistance 10 Ω has a current of 2 A flowing through it. What is the voltage across it?
A5 V
B0.2 V
C20 V
D12 V
Show Answer
✔ C — 20 V
Ohm's Law: V = IR = 2 A × 10 Ω = 20 V
*Why A is wrong:* 5 = R/I = 10/2 — inverted formula.
*Why B is wrong:* 0.2 = I/R = 2/10 — another inverted form.
*Why D is wrong:* 12 = R + I = 10 + 2 — dimensional error (addition of ohms and amperes).
*Why A is wrong:* 5 = R/I = 10/2 — inverted formula.
*Why B is wrong:* 0.2 = I/R = 2/10 — another inverted form.
*Why D is wrong:* 12 = R + I = 10 + 2 — dimensional error (addition of ohms and amperes).
Q061MediumBPSC Prelims
Three resistors of 2 Ω, 3 Ω, and 6 Ω are connected in parallel. What is the equivalent resistance?
A11 Ω
B1 Ω
C0.5 Ω
D6 Ω
Show Answer
✔ B — 1 Ω
For parallel resistors: 1/R = 1/R₁ + 1/R₂ + 1/R₃
1/R = 1/2 + 1/3 + 1/6 = 3/6 + 2/6 + 1/6 = 6/6 = 1
R = 1 Ω
*Why A is wrong:* 11 = 2 + 3 + 6 — this is the series formula, not parallel.
*Why C is wrong:* 0.5 Ω would require 1/R = 2, meaning 1/R values summing to 2.
*Why D is wrong:* 6 Ω is one of the individual resistors, not the parallel combination.
1/R = 1/2 + 1/3 + 1/6 = 3/6 + 2/6 + 1/6 = 6/6 = 1
R = 1 Ω
*Why A is wrong:* 11 = 2 + 3 + 6 — this is the series formula, not parallel.
*Why C is wrong:* 0.5 Ω would require 1/R = 2, meaning 1/R values summing to 2.
*Why D is wrong:* 6 Ω is one of the individual resistors, not the parallel combination.
Q062MediumBPSC Prelims
An electric bulb of 60 W operates at 220 V for 5 hours. What is the electrical energy consumed in kWh?
A0.06 kWh
B0.3 kWh
C60 kWh
D1,100 kWh
Show Answer
✔ B — 0.3 kWh
Energy = Power × Time = 60 W × 5 h = 300 Wh = 0.3 kWh
(1 kWh = 1000 Wh; 300/1000 = 0.3)
*Why A is wrong:* 0.06 = P × 1 h / 1000 — uses 1 hour, not 5.
*Why C is wrong:* 60 kWh = confuses watts with kWh directly (forgets to multiply by hours and divide by 1000).
*Why D is wrong:* 1,100 = P × V = 60 × 220/12 — dimensional error mixing power, voltage.
(1 kWh = 1000 Wh; 300/1000 = 0.3)
*Why A is wrong:* 0.06 = P × 1 h / 1000 — uses 1 hour, not 5.
*Why C is wrong:* 60 kWh = confuses watts with kWh directly (forgets to multiply by hours and divide by 1000).
*Why D is wrong:* 1,100 = P × V = 60 × 220/12 — dimensional error mixing power, voltage.
Q063HardBPSC Prelims
Kirchhoff's Current Law (KCL) states that:
AThe sum of all voltages in a closed loop is zero
BThe algebraic sum of currents at a node (junction) is zero
CCurrent is proportional to voltage in a linear circuit
DElectric power equals voltage squared divided by resistance
Show Answer
✔ B — The algebraic sum of currents at a node (junction) is zero
Kirchhoff's Current Law (KCL): The algebraic sum of all currents meeting at a junction = 0
(i.e., sum of currents entering = sum of currents leaving)
Kirchhoff's Voltage Law (KVL): The algebraic sum of all voltages in a closed loop = 0
*Why A is wrong:* That describes KVL (Voltage Law), not KCL.
*Why C is wrong:* That is Ohm's Law (V = IR for ohmic conductors).
*Why D is wrong:* P = V²/R is the power formula — a derived result, not Kirchhoff's law.
(i.e., sum of currents entering = sum of currents leaving)
Kirchhoff's Voltage Law (KVL): The algebraic sum of all voltages in a closed loop = 0
*Why A is wrong:* That describes KVL (Voltage Law), not KCL.
*Why C is wrong:* That is Ohm's Law (V = IR for ohmic conductors).
*Why D is wrong:* P = V²/R is the power formula — a derived result, not Kirchhoff's law.
Q064HardBPSC Prelims
The resistance of a wire depends on which of the following factors?
ALength only
BCross-sectional area only
CLength, cross-sectional area, and the material (resistivity)
DTemperature only
Show Answer
✔ C — Length, cross-sectional area, and the material (resistivity)
R = ρL/A, where:
- ρ = resistivity (property of the material)
- L = length of wire (R ∝ L — longer wire → more resistance)
- A = cross-sectional area (R ∝ 1/A — thicker wire → less resistance)
Temperature also affects resistance (for metals, R increases with temperature).
*Why A is wrong:* Length is only one factor; material and area also matter.
*Why B is wrong:* Area alone doesn't determine resistance.
*Why D is wrong:* Temperature affects resistance but is not the only factor — and this doesn't include material/geometry.
- ρ = resistivity (property of the material)
- L = length of wire (R ∝ L — longer wire → more resistance)
- A = cross-sectional area (R ∝ 1/A — thicker wire → less resistance)
Temperature also affects resistance (for metals, R increases with temperature).
*Why A is wrong:* Length is only one factor; material and area also matter.
*Why B is wrong:* Area alone doesn't determine resistance.
*Why D is wrong:* Temperature affects resistance but is not the only factor — and this doesn't include material/geometry.
Q065HardBPSC Prelims
A household circuit is protected by a fuse wire. The fuse wire melts when:
AThe voltage in the circuit falls below normal
BThe resistance of the circuit increases
CThe current exceeds the rated value due to short circuit or overload
DThe circuit switch is turned off
Show Answer
✔ C — The current exceeds the rated value due to short circuit or overload
A fuse wire has a low melting point (often lead-tin alloy). When current exceeds the rated value (due to short circuit or overloading), excessive heat (H = I²Rt) is generated. The fuse wire melts and breaks the circuit, preventing fire/damage.
*Why A is wrong:* Low voltage would reduce current — fuse remains intact.
*Why B is wrong:* Higher resistance reduces current (V = IR) — doesn't cause fuse to blow.
*Why D is wrong:* Turning off the switch cuts the circuit; the fuse doesn't melt.
*Why A is wrong:* Low voltage would reduce current — fuse remains intact.
*Why B is wrong:* Higher resistance reduces current (V = IR) — doesn't cause fuse to blow.
*Why D is wrong:* Turning off the switch cuts the circuit; the fuse doesn't melt.
Magnetism
Q066EasyBPSC Prelims
The North pole of a freely suspended bar magnet points toward:
AGeographic South Pole of the Earth
BGeographic North Pole of the Earth
CMagnetic South Pole of the Earth
DEast direction always
Show Answer
✔ B — Geographic North Pole of the Earth
A freely suspended magnet's North pole points toward Earth's Geographic North Pole. This happens because Earth's Geographic North Pole is actually a magnetic south pole (opposite poles attract). The naming is historical/geographic convention.
*Why A is wrong:* The N pole of the magnet points TOWARD geographic NORTH, not south.
*Why C is wrong:* The magnetic south pole of Earth is near the geographic North — so it attracts the compass N — but the answer in practical terms: compass N → geographic North.
*Why D is wrong:* A magnet aligns along the N-S axis, not East-West.
*Why A is wrong:* The N pole of the magnet points TOWARD geographic NORTH, not south.
*Why C is wrong:* The magnetic south pole of Earth is near the geographic North — so it attracts the compass N — but the answer in practical terms: compass N → geographic North.
*Why D is wrong:* A magnet aligns along the N-S axis, not East-West.
Q067MediumBPSC Prelims
An electromagnet differs from a permanent magnet because:
AAn electromagnet can be switched on and off
BAn electromagnet produces a stronger magnetic field always
CAn electromagnet uses no electricity
DA permanent magnet is made of iron only
Show Answer
✔ A — An electromagnet can be switched on and off
Electromagnet: produced by passing current through a coil. When current stops → magnetism stops. This makes it controllable — can be switched ON/OFF.
Permanent magnets: always magnetic, cannot be switched off without physical degaussing.
*Why B is wrong:* Electromagnets can be stronger, but not always — a permanent neodymium magnet can be very strong. The key difference is controllability.
*Why C is wrong:* Electromagnets REQUIRE electricity; permanent magnets do not.
*Why D is wrong:* Permanent magnets are made of steel, alnico, neodymium — not just iron.
Permanent magnets: always magnetic, cannot be switched off without physical degaussing.
*Why B is wrong:* Electromagnets can be stronger, but not always — a permanent neodymium magnet can be very strong. The key difference is controllability.
*Why C is wrong:* Electromagnets REQUIRE electricity; permanent magnets do not.
*Why D is wrong:* Permanent magnets are made of steel, alnico, neodymium — not just iron.
Q068MediumBPSC Prelims
A current-carrying conductor placed in a magnetic field experiences a force. This principle is used in:
ATransformer
BElectric motor
CGenerator
DBattery
Show Answer
✔ B — Electric motor
Electric Motor: uses the force on a current-carrying conductor in a magnetic field (F = BIL × sinθ — Fleming's Left-Hand Rule) to convert electrical energy into mechanical energy (rotation).
Generator: uses the reverse — mechanical motion in a magnetic field to produce current (electromagnetic induction — Fleming's Right-Hand Rule).
*Why A is wrong:* Transformer uses electromagnetic induction (changing magnetic flux) to change voltage levels — not force on current-carrying conductor.
*Why C is wrong:* Generator works on electromagnetic induction (Faraday's law) — conductor moving in field produces current, not the reverse.
*Why D is wrong:* Battery produces EMF by chemical reactions, not magnetic forces.
Generator: uses the reverse — mechanical motion in a magnetic field to produce current (electromagnetic induction — Fleming's Right-Hand Rule).
*Why A is wrong:* Transformer uses electromagnetic induction (changing magnetic flux) to change voltage levels — not force on current-carrying conductor.
*Why C is wrong:* Generator works on electromagnetic induction (Faraday's law) — conductor moving in field produces current, not the reverse.
*Why D is wrong:* Battery produces EMF by chemical reactions, not magnetic forces.
Q069HardBPSC Prelims
Faraday's Law of Electromagnetic Induction states that:
AA moving charge creates a magnetic field
BThe induced EMF in a coil is proportional to the rate of change of magnetic flux through it
CLike poles repel and unlike poles attract
DA current-carrying conductor in a magnetic field experiences a force
Show Answer
✔ B — The induced EMF in a coil is proportional to the rate of change of magnetic flux through it
Faraday's Law: EMF = −dΦ/dt (the induced EMF equals the negative rate of change of magnetic flux Φ through the coil). More flux change per second → more EMF.
Lenz's Law adds: the induced current opposes the change causing it (negative sign).
*Why A is wrong:* Moving charge creating magnetic field is Biot-Savart Law/Ampere's Law.
*Why C is wrong:* That is the basic law of magnetism (poles), not Faraday's law.
*Why D is wrong:* Force on current-carrying conductor is F = BIL — the motor effect (Ampere's force law), not Faraday's law.
Lenz's Law adds: the induced current opposes the change causing it (negative sign).
*Why A is wrong:* Moving charge creating magnetic field is Biot-Savart Law/Ampere's Law.
*Why C is wrong:* That is the basic law of magnetism (poles), not Faraday's law.
*Why D is wrong:* Force on current-carrying conductor is F = BIL — the motor effect (Ampere's force law), not Faraday's law.
Q070HardBPSC Prelims
A transformer has 100 turns in the primary coil and 1000 turns in the secondary coil. If the primary voltage is 220 V, what is the secondary voltage?
A22 V
B2200 V
C220 V
D4400 V
Show Answer
✔ B — 2200 V
Transformer formula: V₂/V₁ = N₂/N₁ (turns ratio = voltage ratio)
V₂ = V₁ × (N₂/N₁) = 220 × (1000/100) = 220 × 10 = 2200 V
Since N₂ > N₁ (step-up transformer), voltage increases.
*Why A is wrong:* 22 = 220/10 — applied step-down formula (divided instead of multiplied).
*Why C is wrong:* 220 = no change — ignores the turns ratio.
*Why D is wrong:* 4400 = 220 × 20 — wrong ratio calculation.
V₂ = V₁ × (N₂/N₁) = 220 × (1000/100) = 220 × 10 = 2200 V
Since N₂ > N₁ (step-up transformer), voltage increases.
*Why A is wrong:* 22 = 220/10 — applied step-down formula (divided instead of multiplied).
*Why C is wrong:* 220 = no change — ignores the turns ratio.
*Why D is wrong:* 4400 = 220 × 20 — wrong ratio calculation.
Atomic Structure & Nuclear Physics
Q071EasyBPSC Prelims
The nucleus of an atom contains:
AProtons and electrons
BProtons and neutrons
CNeutrons and electrons
DOnly protons
Show Answer
✔ B — Protons and neutrons
Atomic structure (Rutherford/Bohr model):
- Nucleus: contains protons (positive charge) and neutrons (no charge)
- Electron cloud: surrounds the nucleus, contains electrons (negative charge)
- Mass is concentrated in nucleus (protons + neutrons)
- Atomic number = number of protons; Mass number = protons + neutrons
*Why A is wrong:* Electrons are NOT in the nucleus — they orbit around it.
*Why C is wrong:* Neutrons are in the nucleus, but electrons are not.
*Why D is wrong:* Nuclei of most elements contain both protons AND neutrons (exception: hydrogen-1 has only 1 proton, no neutrons).
- Nucleus: contains protons (positive charge) and neutrons (no charge)
- Electron cloud: surrounds the nucleus, contains electrons (negative charge)
- Mass is concentrated in nucleus (protons + neutrons)
- Atomic number = number of protons; Mass number = protons + neutrons
*Why A is wrong:* Electrons are NOT in the nucleus — they orbit around it.
*Why C is wrong:* Neutrons are in the nucleus, but electrons are not.
*Why D is wrong:* Nuclei of most elements contain both protons AND neutrons (exception: hydrogen-1 has only 1 proton, no neutrons).
Q072MediumBPSC Prelims
Alpha (α) radiation is stopped by:
AA sheet of paper or a few centimetres of air
BA few millimetres of aluminium sheet
CSeveral centimetres of lead
DCannot be stopped by any material
Show Answer
✔ A — A sheet of paper or a few centimetres of air
Penetrating power of radiations (least to most):
- Alpha (α): least penetrating — stopped by paper, skin, or a few cm of air. (Large particle: 2 protons + 2 neutrons)
- Beta (β): moderate — stopped by a few mm of aluminium
- Gamma (γ): most penetrating — requires several cm of lead or metres of concrete
*Why B is wrong:* Aluminium stops beta radiation, not alpha.
*Why C is wrong:* Lead shielding is needed for gamma radiation.
*Why D is wrong:* Alpha is the easiest to stop — paper is sufficient.
- Alpha (α): least penetrating — stopped by paper, skin, or a few cm of air. (Large particle: 2 protons + 2 neutrons)
- Beta (β): moderate — stopped by a few mm of aluminium
- Gamma (γ): most penetrating — requires several cm of lead or metres of concrete
*Why B is wrong:* Aluminium stops beta radiation, not alpha.
*Why C is wrong:* Lead shielding is needed for gamma radiation.
*Why D is wrong:* Alpha is the easiest to stop — paper is sufficient.
Q073MediumBPSC Prelims
Which of the following correctly distinguishes nuclear fission from nuclear fusion?
AFission = joining of light nuclei; Fusion = splitting of heavy nuclei
BFission = splitting of heavy nuclei; Fusion = joining of light nuclei
CBoth fission and fusion release energy; fission occurs in stars
DFusion requires uranium; fission requires hydrogen
Show Answer
✔ B — Fission = splitting of heavy nuclei; Fusion = joining of light nuclei
- Nuclear Fission: splitting of a heavy nucleus (e.g., U-235) into two smaller nuclei + energy + neutrons. Used in nuclear power plants and atomic bombs.
- Nuclear Fusion: joining of two light nuclei (e.g., H + H → He) to form a heavier nucleus + enormous energy. Powers the Sun and stars; being developed for fusion reactors.
*Why A is wrong:* This reverses the definitions — fission is splitting, fusion is joining.
*Why C is wrong:* Fusion occurs in stars (not fission); both do release energy but the statement about "fission in stars" is wrong.
*Why D is wrong:* Fusion requires hydrogen isotopes (deuterium/tritium); fission uses uranium or plutonium.
- Nuclear Fusion: joining of two light nuclei (e.g., H + H → He) to form a heavier nucleus + enormous energy. Powers the Sun and stars; being developed for fusion reactors.
*Why A is wrong:* This reverses the definitions — fission is splitting, fusion is joining.
*Why C is wrong:* Fusion occurs in stars (not fission); both do release energy but the statement about "fission in stars" is wrong.
*Why D is wrong:* Fusion requires hydrogen isotopes (deuterium/tritium); fission uses uranium or plutonium.
Q074MediumBPSC Prelims
The half-life of a radioactive substance is 10 years. After 30 years, what fraction of the original sample remains?
A1/2
B1/4
C1/8
D1/3
Show Answer
✔ C — 1/8
After each half-life, the amount remaining = half the previous amount.
Number of half-lives in 30 years = 30/10 = 3
After 1 half-life: 1/2 remains
After 2 half-lives: 1/4 remains
After 3 half-lives: 1/8 remains
Formula: N = N₀ × (1/2)^n where n = number of half-lives = 3
N/N₀ = (1/2)³ = 1/8 ✓
*Why A is wrong:* 1/2 is after only 1 half-life (10 years).
*Why B is wrong:* 1/4 is after 2 half-lives (20 years).
*Why D is wrong:* 1/3 doesn't correspond to any integer number of half-lives.
Number of half-lives in 30 years = 30/10 = 3
After 1 half-life: 1/2 remains
After 2 half-lives: 1/4 remains
After 3 half-lives: 1/8 remains
Formula: N = N₀ × (1/2)^n where n = number of half-lives = 3
N/N₀ = (1/2)³ = 1/8 ✓
*Why A is wrong:* 1/2 is after only 1 half-life (10 years).
*Why B is wrong:* 1/4 is after 2 half-lives (20 years).
*Why D is wrong:* 1/3 doesn't correspond to any integer number of half-lives.
Q075HardBPSC Prelims
Einstein's mass-energy equivalence formula E = mc² implies:
AMass and energy are completely unrelated
BA small amount of mass can be converted into an enormous amount of energy
CEnergy is always equal to mass
DOnly nuclear reactions can convert mass to energy
Show Answer
✔ B — A small amount of mass can be converted into an enormous amount of energy
E = mc², where c = 3 × 10⁸ m/s (speed of light). Since c² is extremely large (9 × 10¹⁶ m²/s²), even a small mass m converts to enormous energy.
Example: 1 gram = 0.001 kg → E = 0.001 × (3×10⁸)² = 9 × 10¹³ J — enough to power a city for days.
*Why A is wrong:* E = mc² is precisely about the equivalence of mass and energy.
*Why C is wrong:* E ≠ m; they're related by the factor c², not equal (different dimensions).
*Why D is wrong:* Mass-energy conversion also occurs in pair production, matter-antimatter annihilation, and is conceptually universal.
Example: 1 gram = 0.001 kg → E = 0.001 × (3×10⁸)² = 9 × 10¹³ J — enough to power a city for days.
*Why A is wrong:* E = mc² is precisely about the equivalence of mass and energy.
*Why C is wrong:* E ≠ m; they're related by the factor c², not equal (different dimensions).
*Why D is wrong:* Mass-energy conversion also occurs in pair production, matter-antimatter annihilation, and is conceptually universal.
Q076HardBPSC Prelims
Which of the following is used as a moderator in a nuclear reactor to slow down fast neutrons?
AUranium-235
BPlutonium-239
CHeavy water (D₂O) or graphite
DCadmium rods
Show Answer
✔ C — Heavy water (D₂O) or graphite
In a nuclear reactor:
- Fuel: enriched Uranium-235 or Plutonium-239 (fissile materials)
- Moderator: heavy water (D₂O), graphite, or light water — slows down fast neutrons to thermal speeds to sustain chain reaction
- Control rods: cadmium or boron rods — absorb neutrons to control reaction rate
- Coolant: water or CO₂ — carries heat to generate steam
*Why A is wrong:* U-235 is the fissile fuel, not the moderator.
*Why B is wrong:* Pu-239 is another nuclear fuel (bred from U-238), not a moderator.
*Why D is wrong:* Cadmium rods are control rods (absorb neutrons), not moderators.
- Fuel: enriched Uranium-235 or Plutonium-239 (fissile materials)
- Moderator: heavy water (D₂O), graphite, or light water — slows down fast neutrons to thermal speeds to sustain chain reaction
- Control rods: cadmium or boron rods — absorb neutrons to control reaction rate
- Coolant: water or CO₂ — carries heat to generate steam
*Why A is wrong:* U-235 is the fissile fuel, not the moderator.
*Why B is wrong:* Pu-239 is another nuclear fuel (bred from U-238), not a moderator.
*Why D is wrong:* Cadmium rods are control rods (absorb neutrons), not moderators.
Q077HardBPSC Prelims
Gamma radiation is used for sterilising medical equipment because:
AIt heats the equipment to kill bacteria
BIt has high penetrating power and can kill microorganisms without damaging packaging
CIt is the cheapest form of radiation
DIt changes the chemical composition of bacteria
Show Answer
✔ B — It has high penetrating power and can kill microorganisms without damaging packaging
Gamma radiation has the highest penetrating power — it can pass through sealed packaging and kill bacteria, viruses, and other microorganisms by damaging their DNA. Medical supplies can be sterilised without opening/exposing them to heat or chemicals.
*Why A is wrong:* Gamma doesn't sterilise by heating — it uses ionising radiation to damage DNA.
*Why C is wrong:* Cost is not the primary reason; gamma's high penetration through packaging is the key advantage.
*Why D is wrong:* Gamma kills bacteria by ionising radiation damaging DNA (cell killing, not chemical composition change in bacteria's structural sense).
*Why A is wrong:* Gamma doesn't sterilise by heating — it uses ionising radiation to damage DNA.
*Why C is wrong:* Cost is not the primary reason; gamma's high penetration through packaging is the key advantage.
*Why D is wrong:* Gamma kills bacteria by ionising radiation damaging DNA (cell killing, not chemical composition change in bacteria's structural sense).
Optics — Lenses & Mirrors
Q078EasyBPSC Prelims
A convex lens is also called a:
ADiverging lens
BConcave lens
CConverging lens
DPlano-concave lens
Show Answer
✔ C — Converging lens
A convex lens is thicker at the centre and thinner at the edges. It brings parallel rays of light to a focus → converging lens.
A concave lens is thinner at the centre → diverges light → diverging lens.
*Why A is wrong:* Diverging describes a concave lens.
*Why B is wrong:* Concave lens is a different type — thinner at centre.
*Why D is wrong:* Plano-concave = flat on one side, concave on other — not a synonym for convex.
A concave lens is thinner at the centre → diverges light → diverging lens.
*Why A is wrong:* Diverging describes a concave lens.
*Why B is wrong:* Concave lens is a different type — thinner at centre.
*Why D is wrong:* Plano-concave = flat on one side, concave on other — not a synonym for convex.
Q079MediumBPSC Prelims
A convex lens of focal length 25 cm is used as a simple microscope. An object is placed at 20 cm from the lens. Where is the image?
AAt infinity
B100 cm on the same side as the object (virtual, upright)
C100 cm on the opposite side (real, inverted)
D20 cm on the opposite side
Show Answer
✔ B — 100 cm on the same side as the object (virtual, upright)
Lens formula: 1/v − 1/u = 1/f (using sign convention: u = −20, f = +25)
1/v = 1/f + 1/u = 1/25 + 1/(−20) = 4/100 − 5/100 = −1/100
v = −100 cm
Negative sign means image is on the same side as the object → virtual, upright, 100 cm from lens. Magnified image — this is how a simple microscope (magnifying glass) works when object is within focal length.
*Why A is wrong:* Image at infinity occurs when object is exactly at the focal point (u = −25 here, not −20).
*Why C is wrong:* Real inverted image on the other side occurs when object is beyond the focal length.
*Why D is wrong:* 20 cm on opposite side would require specific calculation — doesn't match.
1/v = 1/f + 1/u = 1/25 + 1/(−20) = 4/100 − 5/100 = −1/100
v = −100 cm
Negative sign means image is on the same side as the object → virtual, upright, 100 cm from lens. Magnified image — this is how a simple microscope (magnifying glass) works when object is within focal length.
*Why A is wrong:* Image at infinity occurs when object is exactly at the focal point (u = −25 here, not −20).
*Why C is wrong:* Real inverted image on the other side occurs when object is beyond the focal length.
*Why D is wrong:* 20 cm on opposite side would require specific calculation — doesn't match.
Q080MediumBPSC Prelims
The power of a lens is +4 dioptres. This lens is:
AConcave, with focal length 25 cm
BConvex, with focal length 25 cm
CConcave, with focal length 4 cm
DConvex, with focal length 4 m
Show Answer
✔ B — Convex, with focal length 25 cm
Power P = 1/f (where f is in metres)
f = 1/P = 1/4 = 0.25 m = 25 cm
Positive power (+4 D) → converging (convex) lens
Negative power → diverging (concave) lens
*Why A is wrong:* Positive power means convex (converging) lens, not concave.
*Why C is wrong:* 4 cm would require P = 1/0.04 = 25 D — not 4 D.
*Why D is wrong:* 4 m focal length would give P = 0.25 D — not 4 D.
f = 1/P = 1/4 = 0.25 m = 25 cm
Positive power (+4 D) → converging (convex) lens
Negative power → diverging (concave) lens
*Why A is wrong:* Positive power means convex (converging) lens, not concave.
*Why C is wrong:* 4 cm would require P = 1/0.04 = 25 D — not 4 D.
*Why D is wrong:* 4 m focal length would give P = 0.25 D — not 4 D.
Q081MediumBPSC Prelims
A person cannot see objects clearly beyond 1 metre. What type of defect does this person have, and what corrective lens is needed?
AHypermetropia; convex lens
BMyopia; concave lens
CPresbyopia; bifocal lens
DAstigmatism; cylindrical lens
Show Answer
✔ B — Myopia; concave lens
Myopia (short-sightedness): person can see near objects clearly but cannot see distant objects (far point < infinity — in this case, 1 m). Image forms in front of the retina.
Correction: Concave (diverging) lens — moves the image back to the retina.
*Why A is wrong:* Hypermetropia is long-sightedness (cannot see near objects clearly) — corrected by convex lens.
*Why C is wrong:* Presbyopia is age-related loss of near-vision accommodation — corrected by bifocals.
*Why D is wrong:* Astigmatism is due to irregular cornea curvature — corrected by cylindrical/toric lens.
Correction: Concave (diverging) lens — moves the image back to the retina.
*Why A is wrong:* Hypermetropia is long-sightedness (cannot see near objects clearly) — corrected by convex lens.
*Why C is wrong:* Presbyopia is age-related loss of near-vision accommodation — corrected by bifocals.
*Why D is wrong:* Astigmatism is due to irregular cornea curvature — corrected by cylindrical/toric lens.
Q082HardBPSC Prelims
A compound microscope has an objective lens of focal length 1 cm and an eyepiece of focal length 5 cm. The final image is formed at infinity. The tube length is 10 cm. What is the total magnification?
A50×
B100×
C30×
D10×
Show Answer
✔ A — 50×
Magnification of compound microscope (image at infinity):
M = (L/f_o) × (D/f_e)
where L = tube length = 10 cm; f_o = 1 cm; D = 25 cm (near point); f_e = 5 cm
M = (10/1) × (25/5) = 10 × 5 = 50×
*Why B is wrong:* 100× would require tube length of 20 cm or different focal lengths.
*Why C is wrong:* 30× = (10/1) × (25/25/3) — wrong calculation.
*Why D is wrong:* 10× is the objective magnification alone, without the eyepiece.
M = (L/f_o) × (D/f_e)
where L = tube length = 10 cm; f_o = 1 cm; D = 25 cm (near point); f_e = 5 cm
M = (10/1) × (25/5) = 10 × 5 = 50×
*Why B is wrong:* 100× would require tube length of 20 cm or different focal lengths.
*Why C is wrong:* 30× = (10/1) × (25/25/3) — wrong calculation.
*Why D is wrong:* 10× is the objective magnification alone, without the eyepiece.
Q083HardBPSC Prelims
Two thin lenses of focal lengths f₁ = 10 cm and f₂ = −20 cm are placed in contact. What is the effective focal length of the combination?
A10 cm
B−20 cm
C20 cm
D30 cm
Show Answer
✔ C — 20 cm
For lenses in contact: 1/f = 1/f₁ + 1/f₂
1/f = 1/10 + 1/(−20) = 2/20 − 1/20 = 1/20
f = 20 cm (positive → converging combination)
*Why A is wrong:* 10 cm is the focal length of the first lens alone.
*Why B is wrong:* −20 cm is the second (concave) lens focal length; combined lens is different.
*Why D is wrong:* 30 cm would give 1/f = 1/10 + 1/20 — incorrect signs.
1/f = 1/10 + 1/(−20) = 2/20 − 1/20 = 1/20
f = 20 cm (positive → converging combination)
*Why A is wrong:* 10 cm is the focal length of the first lens alone.
*Why B is wrong:* −20 cm is the second (concave) lens focal length; combined lens is different.
*Why D is wrong:* 30 cm would give 1/f = 1/10 + 1/20 — incorrect signs.
Q084HardBPSC Prelims
A rainbow is formed due to which combination of phenomena?
AOnly reflection of sunlight in water droplets
BDispersion, refraction, and total internal reflection in water droplets
CDiffraction of sunlight around water droplets
DAbsorption of sunlight by water vapour and re-emission
Show Answer
✔ B — Dispersion, refraction, and total internal reflection in water droplets
Rainbow formation in water droplets involves THREE steps:
1. Refraction at entry into the droplet (light bends + dispersion begins)
2. Total Internal Reflection inside the back of the droplet (light reflects back)
3. Refraction again at exit (more dispersion, colours spread out)
The combination creates the spectrum of VIBGYOR with red on outside (40–42°) and violet inside (40–42° — slightly different angle).
*Why A is wrong:* Reflection alone doesn't cause colour separation (dispersion).
*Why C is wrong:* Diffraction produces different colour patterns — not the cause of rainbow.
*Why D is wrong:* Water doesn't absorb and re-emit specific colours of sunlight.
1. Refraction at entry into the droplet (light bends + dispersion begins)
2. Total Internal Reflection inside the back of the droplet (light reflects back)
3. Refraction again at exit (more dispersion, colours spread out)
The combination creates the spectrum of VIBGYOR with red on outside (40–42°) and violet inside (40–42° — slightly different angle).
*Why A is wrong:* Reflection alone doesn't cause colour separation (dispersion).
*Why C is wrong:* Diffraction produces different colour patterns — not the cause of rainbow.
*Why D is wrong:* Water doesn't absorb and re-emit specific colours of sunlight.
Simple Machines, Inertia, Centripetal Force
Q085EasyBPSC Prelims
Which of the following is an example of a lever of the Third Class?
AA see-saw (teeter-totter)
BWheelbarrow
CForceps (tweezers)
DScissor
Show Answer
✔ C — Forceps (tweezers)
Levers classified by position of Fulcrum (F), Effort (E), Load (L):
- Class I: F between E and L (see-saw, scissors, pliers)
- Class II: L between F and E (wheelbarrow, bottle opener, nutcracker)
- Class III: E between F and L (forceps/tweezers, fishing rod, broom sweeping)
In forceps, the fulcrum is at the top (hinge), load is at the tip, effort is applied in the middle → Class III
*Why A is wrong:* See-saw is Class I (fulcrum in middle).
*Why B is wrong:* Wheelbarrow is Class II (load between fulcrum and effort).
*Why D is wrong:* Scissors are Class I.
- Class I: F between E and L (see-saw, scissors, pliers)
- Class II: L between F and E (wheelbarrow, bottle opener, nutcracker)
- Class III: E between F and L (forceps/tweezers, fishing rod, broom sweeping)
In forceps, the fulcrum is at the top (hinge), load is at the tip, effort is applied in the middle → Class III
*Why A is wrong:* See-saw is Class I (fulcrum in middle).
*Why B is wrong:* Wheelbarrow is Class II (load between fulcrum and effort).
*Why D is wrong:* Scissors are Class I.
Q086MediumBPSC Prelims
A pulley system with mechanical advantage 4 is used to lift a 200 kg load. What is the effort force required? (g = 10 m/s²)
A800 N
B200 N
C50 N
D500 N
Show Answer
✔ D — 500 N
Load force = mg = 200 × 10 = 2000 N
Mechanical Advantage (MA) = Load/Effort
Effort = Load/MA = 2000/4 = 500 N
*Why A is wrong:* 800 N = Load/2.5 — wrong MA value.
*Why B is wrong:* 200 N = mass only (forgot to multiply by g).
*Why C is wrong:* 50 N = 200/(4×10) — divided by both MA and g separately (double division).
Mechanical Advantage (MA) = Load/Effort
Effort = Load/MA = 2000/4 = 500 N
*Why A is wrong:* 800 N = Load/2.5 — wrong MA value.
*Why B is wrong:* 200 N = mass only (forgot to multiply by g).
*Why C is wrong:* 50 N = 200/(4×10) — divided by both MA and g separately (double division).
Q087MediumBPSC Prelims
An object moving in a circular path requires centripetal force directed:
AAway from the centre (centrifugal — outward)
BTangentially to the circle
CToward the centre of the circle
DPerpendicular to the plane of the circle
Show Answer
✔ C — Toward the centre of the circle
Centripetal force: the net force directed toward the centre of the circular path, required to keep an object moving in a circle. Without it, the object would fly off tangentially (Newton's First Law).
Formula: F = mv²/r (directed inward)
Centrifugal force is a pseudo-force felt in a rotating frame — it doesn't actually exist in an inertial frame.
*Why A is wrong:* Centrifugal force is pseudo (fictitious in rotating frame); the real force is centripetal (inward).
*Why B is wrong:* Tangential force causes change in speed (not direction for circular motion).
*Why D is wrong:* Force perpendicular to the plane would cause the object to move out of the plane.
Formula: F = mv²/r (directed inward)
Centrifugal force is a pseudo-force felt in a rotating frame — it doesn't actually exist in an inertial frame.
*Why A is wrong:* Centrifugal force is pseudo (fictitious in rotating frame); the real force is centripetal (inward).
*Why B is wrong:* Tangential force causes change in speed (not direction for circular motion).
*Why D is wrong:* Force perpendicular to the plane would cause the object to move out of the plane.
Q088MediumBPSC Prelims
Why does a spinning top not fall over while rotating?
ACentripetal force keeps it balanced
BAngular momentum resists any change in orientation (gyroscopic effect)
CFriction from the ground keeps it upright
DThe top's weight is balanced by the centrifugal force
Show Answer
✔ B — Angular momentum resists any change in orientation (gyroscopic effect)
A spinning top has angular momentum (L = Iω). By conservation of angular momentum, a rotating body resists change in its axis of rotation — this is the gyroscopic effect. The top precesses slowly instead of toppling.
When spin slows down → angular momentum decreases → gyroscopic effect weakens → top falls.
*Why A is wrong:* Centripetal force keeps the body on a circular path — not relevant to the top staying upright.
*Why C is wrong:* Friction from the ground helps the top spin but doesn't directly cause it to stay upright.
*Why D is wrong:* Centrifugal force is a pseudo-force; the top doesn't "balance" weight this way — gyroscopic precession is the real explanation.
When spin slows down → angular momentum decreases → gyroscopic effect weakens → top falls.
*Why A is wrong:* Centripetal force keeps the body on a circular path — not relevant to the top staying upright.
*Why C is wrong:* Friction from the ground helps the top spin but doesn't directly cause it to stay upright.
*Why D is wrong:* Centrifugal force is a pseudo-force; the top doesn't "balance" weight this way — gyroscopic precession is the real explanation.
Q089HardBPSC Prelims
A satellite orbits Earth at a height where the orbital speed is 7.9 km/s. If the height is increased, the orbital speed:
AIncreases, because more centripetal force is needed at higher altitude
BDecreases, because gravitational force is weaker at greater height
CRemains the same, because gravity provides exactly the needed centripetal force
DIncreases, because the satellite has more potential energy
Show Answer
✔ B — Decreases, because gravitational force is weaker at greater height
Orbital speed v = √(GM/r), where r = (R_Earth + height) and GM is the gravitational parameter.
As height increases → r increases → v = √(GM/r) decreases.
Higher orbits have slower orbital speeds (though longer periods — Kepler's 3rd Law).
Example: ISS (400 km altitude) ≈ 7.7 km/s; GPS satellites (20,200 km) ≈ 3.9 km/s; Geostationary (35,786 km) ≈ 3.07 km/s.
*Why A is wrong:* At higher altitude, gravity is weaker — less centripetal force needed; orbital speed decreases.
*Why C is wrong:* Orbital speed does change with altitude — it's not constant.
*Why D is wrong:* More potential energy doesn't increase orbital speed — it actually trades against kinetic energy.
As height increases → r increases → v = √(GM/r) decreases.
Higher orbits have slower orbital speeds (though longer periods — Kepler's 3rd Law).
Example: ISS (400 km altitude) ≈ 7.7 km/s; GPS satellites (20,200 km) ≈ 3.9 km/s; Geostationary (35,786 km) ≈ 3.07 km/s.
*Why A is wrong:* At higher altitude, gravity is weaker — less centripetal force needed; orbital speed decreases.
*Why C is wrong:* Orbital speed does change with altitude — it's not constant.
*Why D is wrong:* More potential energy doesn't increase orbital speed — it actually trades against kinetic energy.
Q090HardBPSC Prelims
The escape velocity from Earth's surface is approximately 11.2 km/s. The escape velocity from the Moon is much lower because:
AThe Moon is smaller and lighter than Earth, so its gravitational pull is weaker
BThe Moon is farther from the Sun
CThe Moon has no atmosphere
DThe Moon rotates more slowly
Show Answer
✔ A — The Moon is smaller and lighter than Earth, so its gravitational pull is weaker
Escape velocity v_e = √(2GM/R)
For the Moon: mass M_Moon ≈ 1/81 × M_Earth; radius R_Moon ≈ 1/3.7 × R_Earth
v_e_Moon = √(2G × M_Moon / R_Moon) ≈ 2.38 km/s (vs 11.2 km/s for Earth)
The combination of lower mass AND smaller radius gives the Moon a much lower escape velocity.
*Why B is wrong:* Distance from Sun doesn't directly affect the Moon's own escape velocity (which depends on Moon's own M and R).
*Why C is wrong:* No atmosphere doesn't affect escape velocity — it affects atmospheric drag but not the gravitational calculation.
*Why D is wrong:* Rotation speed ≠ escape velocity; these are independent properties.
For the Moon: mass M_Moon ≈ 1/81 × M_Earth; radius R_Moon ≈ 1/3.7 × R_Earth
v_e_Moon = √(2G × M_Moon / R_Moon) ≈ 2.38 km/s (vs 11.2 km/s for Earth)
The combination of lower mass AND smaller radius gives the Moon a much lower escape velocity.
*Why B is wrong:* Distance from Sun doesn't directly affect the Moon's own escape velocity (which depends on Moon's own M and R).
*Why C is wrong:* No atmosphere doesn't affect escape velocity — it affects atmospheric drag but not the gravitational calculation.
*Why D is wrong:* Rotation speed ≠ escape velocity; these are independent properties.
Q091HardBPSC Prelims
A figure skater pulling their arms inward while spinning speeds up. This demonstrates:
AConservation of linear momentum
BIncrease in centripetal force
CConservation of angular momentum
DIncrease in kinetic energy from an external source
Show Answer
✔ C — Conservation of angular momentum
When the skater pulls arms inward:
- Moment of inertia (I) decreases (mass concentrated closer to axis)
- Angular momentum L = Iω = constant (no external torque)
- Therefore: ω increases (spins faster)
L₁ = L₂ → I₁ω₁ = I₂ω₂ → if I decreases, ω must increase.
*Why A is wrong:* Linear momentum is not relevant here; the motion is rotational.
*Why B is wrong:* Centripetal force changes, but the principle at work is angular momentum conservation.
*Why D is wrong:* No external energy source — kinetic energy actually increases (from work done by arms pulling inward), but the governing principle is L conservation.
- Moment of inertia (I) decreases (mass concentrated closer to axis)
- Angular momentum L = Iω = constant (no external torque)
- Therefore: ω increases (spins faster)
L₁ = L₂ → I₁ω₁ = I₂ω₂ → if I decreases, ω must increase.
*Why A is wrong:* Linear momentum is not relevant here; the motion is rotational.
*Why B is wrong:* Centripetal force changes, but the principle at work is angular momentum conservation.
*Why D is wrong:* No external energy source — kinetic energy actually increases (from work done by arms pulling inward), but the governing principle is L conservation.
Units, Measurement, Gravity
Q092EasyBPSC Prelims
The SI unit of force is:
AJoule
BPascal
CNewton
DWatt
Show Answer
✔ C — Newton
SI Units:
- Force: Newton (N) = kg⋅m/s²
- Energy/Work: Joule (J) = kg⋅m²/s² = N⋅m
- Pressure: Pascal (Pa) = N/m²
- Power: Watt (W) = J/s
1 Newton = force required to give 1 kg mass an acceleration of 1 m/s²
*Why A is wrong:* Joule is the unit of energy/work, not force.
*Why B is wrong:* Pascal is the unit of pressure (force per area).
*Why D is wrong:* Watt is the unit of power (energy per time).
- Force: Newton (N) = kg⋅m/s²
- Energy/Work: Joule (J) = kg⋅m²/s² = N⋅m
- Pressure: Pascal (Pa) = N/m²
- Power: Watt (W) = J/s
1 Newton = force required to give 1 kg mass an acceleration of 1 m/s²
*Why A is wrong:* Joule is the unit of energy/work, not force.
*Why B is wrong:* Pascal is the unit of pressure (force per area).
*Why D is wrong:* Watt is the unit of power (energy per time).
Q093MediumBPSC Prelims
Dimensional analysis is used to:
AMeasure the size of molecules
BCheck the correctness of physical equations and convert units
CDetermine the mass of particles
DFind the atomic number of elements
Show Answer
✔ B — Check the correctness of physical equations and convert units
Dimensional analysis uses fundamental dimensions (M = mass, L = length, T = time, etc.) to:
1. Check equation correctness: both sides must have same dimensions
2. Derive formulae: by matching dimensions
3. Unit conversion: between different system of units (SI to CGS etc.)
Example: Check v = u + at: [LT⁻¹] = [LT⁻¹] + [LT⁻²][T] = [LT⁻¹] ✓
*Why A is wrong:* Molecular size is measured by X-ray diffraction, electron microscopy — not dimensional analysis.
*Why C is wrong:* Particle mass requires mass spectrometry or particle physics experiments.
*Why D is wrong:* Atomic number is determined by nuclear charge/electron count — chemistry/nuclear physics.
1. Check equation correctness: both sides must have same dimensions
2. Derive formulae: by matching dimensions
3. Unit conversion: between different system of units (SI to CGS etc.)
Example: Check v = u + at: [LT⁻¹] = [LT⁻¹] + [LT⁻²][T] = [LT⁻¹] ✓
*Why A is wrong:* Molecular size is measured by X-ray diffraction, electron microscopy — not dimensional analysis.
*Why C is wrong:* Particle mass requires mass spectrometry or particle physics experiments.
*Why D is wrong:* Atomic number is determined by nuclear charge/electron count — chemistry/nuclear physics.
Q094MediumBPSC Prelims
Which of the following instruments is used to measure atmospheric pressure?
AHygrometer
BThermometer
CBarometer
DAnemometer
Show Answer
✔ C — Barometer
- Barometer: measures atmospheric pressure
- Thermometer: measures temperature
- Hygrometer: measures humidity (moisture content of air)
- Anemometer: measures wind speed
Standard atmosphere = 101,325 Pa = 760 mm Hg (mercury barometer reading at sea level).
*Why A is wrong:* Hygrometer measures humidity — important for weather, not pressure.
*Why B is wrong:* Thermometer measures temperature.
*Why D is wrong:* Anemometer measures wind speed — used in weather stations.
- Thermometer: measures temperature
- Hygrometer: measures humidity (moisture content of air)
- Anemometer: measures wind speed
Standard atmosphere = 101,325 Pa = 760 mm Hg (mercury barometer reading at sea level).
*Why A is wrong:* Hygrometer measures humidity — important for weather, not pressure.
*Why B is wrong:* Thermometer measures temperature.
*Why D is wrong:* Anemometer measures wind speed — used in weather stations.
Q095MediumBPSC Prelims
The value of acceleration due to gravity (g) is maximum at:
AThe equator
BThe poles
CThe tropics
DThe same everywhere on Earth
Show Answer
✔ B — The poles
g varies on Earth's surface because:
1. Earth is not a perfect sphere (slightly flattened at poles → Earth's poles are closer to the centre → stronger gravity)
2. Rotation of Earth (centrifugal effect at equator reduces effective g)
Result: g_pole ≈ 9.832 m/s² > g_equator ≈ 9.780 m/s²
*Why A is wrong:* g is minimum at the equator (farthest from centre, centrifugal effect maximum).
*Why C is wrong:* Tropics are between equator and poles; g is intermediate.
*Why D is wrong:* g varies with latitude and altitude — not uniform everywhere.
1. Earth is not a perfect sphere (slightly flattened at poles → Earth's poles are closer to the centre → stronger gravity)
2. Rotation of Earth (centrifugal effect at equator reduces effective g)
Result: g_pole ≈ 9.832 m/s² > g_equator ≈ 9.780 m/s²
*Why A is wrong:* g is minimum at the equator (farthest from centre, centrifugal effect maximum).
*Why C is wrong:* Tropics are between equator and poles; g is intermediate.
*Why D is wrong:* g varies with latitude and altitude — not uniform everywhere.
Q096HardBPSC Prelims
A body is projected upward at 45° to the horizontal with a velocity of 20 m/s. What is the maximum range? (g = 10 m/s²)
A20 m
B40 m
C400 m
D10 m
Show Answer
✔ B — 40 m
Range of projectile: R = v²sin(2θ)/g
At θ = 45°: sin(90°) = 1 (maximum range condition)
R = (20)² × 1 / 10 = 400/10 = 40 m
Maximum range is achieved at 45° of projection.
*Why A is wrong:* 20 m = v²/(2g) × 1 — half the correct formula result.
*Why C is wrong:* 400 = v² only — forgot to divide by g.
*Why D is wrong:* 10 m = g = some confusion of values.
At θ = 45°: sin(90°) = 1 (maximum range condition)
R = (20)² × 1 / 10 = 400/10 = 40 m
Maximum range is achieved at 45° of projection.
*Why A is wrong:* 20 m = v²/(2g) × 1 — half the correct formula result.
*Why C is wrong:* 400 = v² only — forgot to divide by g.
*Why D is wrong:* 10 m = g = some confusion of values.
Q097HardBPSC Prelims
A satellite in a circular orbit does no work against Earth's gravity because:
AGravity is absent in orbit
BThe gravitational force is always perpendicular to the satellite's velocity
CThe satellite moves in a straight line
DSatellites generate their own energy
Show Answer
✔ B — The gravitational force is always perpendicular to the satellite's velocity
Work = F × d × cosθ. For a circular orbit:
- Gravitational force is directed radially inward (toward Earth's centre)
- Satellite's velocity is tangential (perpendicular to radius)
- Angle between force and velocity = 90°; cos90° = 0
- Therefore, W = F × d × 0 = zero
Gravity does zero work on the satellite in a circular orbit, even though the satellite is continuously moving.
*Why A is wrong:* Gravity is NOT absent in orbit — it IS the centripetal force keeping the satellite in orbit (g ≈ 8.7 m/s² at ISS altitude).
*Why C is wrong:* Satellites move in curves (circular/elliptical), not straight lines.
*Why D is wrong:* Satellites don't generate energy — this is physically incorrect.
- Gravitational force is directed radially inward (toward Earth's centre)
- Satellite's velocity is tangential (perpendicular to radius)
- Angle between force and velocity = 90°; cos90° = 0
- Therefore, W = F × d × 0 = zero
Gravity does zero work on the satellite in a circular orbit, even though the satellite is continuously moving.
*Why A is wrong:* Gravity is NOT absent in orbit — it IS the centripetal force keeping the satellite in orbit (g ≈ 8.7 m/s² at ISS altitude).
*Why C is wrong:* Satellites move in curves (circular/elliptical), not straight lines.
*Why D is wrong:* Satellites don't generate energy — this is physically incorrect.
Miscellaneous Physics
Q098MediumBPSC Prelims
The pressure at the bottom of a liquid column of height h, density ρ, under gravity g is:
Aρ/gh
Bρg/h
Cρgh
Dh/(ρg)
Show Answer
✔ C — ρgh
Pressure at depth h in a liquid = ρgh (Pascal's principle)
- ρ = density of liquid (kg/m³)
- g = acceleration due to gravity (m/s²)
- h = depth below surface (m)
- Units: kg/m³ × m/s² × m = kg/(m·s²) = Pa ✓
*Why A is wrong:* ρ/gh has wrong dimensions (kg/(m³) ÷ (m/s² × m)) — not pascals.
*Why B is wrong:* ρg/h → kg/(m³·s²) — not pressure dimensions.
*Why D is wrong:* h/(ρg) → m × m³ × s²/kg — dimensional error.
- ρ = density of liquid (kg/m³)
- g = acceleration due to gravity (m/s²)
- h = depth below surface (m)
- Units: kg/m³ × m/s² × m = kg/(m·s²) = Pa ✓
*Why A is wrong:* ρ/gh has wrong dimensions (kg/(m³) ÷ (m/s² × m)) — not pascals.
*Why B is wrong:* ρg/h → kg/(m³·s²) — not pressure dimensions.
*Why D is wrong:* h/(ρg) → m × m³ × s²/kg — dimensional error.
Q099MediumBPSC Prelims
Archimedes' principle states that when a body is immersed in a fluid:
AThe body sinks if its density is greater than water
BIt experiences an upward buoyant force equal to the weight of fluid displaced
CThe pressure on the body is ρgh from all directions
DThe body floats if its volume equals the volume of fluid
Show Answer
✔ B — It experiences an upward buoyant force equal to the weight of fluid displaced
Archimedes' Principle: Any body fully or partially submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced.
F_buoyancy = ρ_fluid × V_displaced × g
Applications: floating ships, submarines, hot air balloons, lactometer (testing milk purity), hydrometer (measuring liquid density).
*Why A is wrong:* While true (sinking condition), it's not Archimedes' principle itself — that's an application/consequence.
*Why C is wrong:* Pressure p = ρgh describes pressure at a point — related but distinct from buoyancy principle.
*Why D is wrong:* Floating occurs when weight = buoyant force (not when volumes are equal).
F_buoyancy = ρ_fluid × V_displaced × g
Applications: floating ships, submarines, hot air balloons, lactometer (testing milk purity), hydrometer (measuring liquid density).
*Why A is wrong:* While true (sinking condition), it's not Archimedes' principle itself — that's an application/consequence.
*Why C is wrong:* Pressure p = ρgh describes pressure at a point — related but distinct from buoyancy principle.
*Why D is wrong:* Floating occurs when weight = buoyant force (not when volumes are equal).
Q100HardBPSC Prelims
Bernoulli's principle states that in a streamline flow of an ideal fluid, as the speed of the fluid increases:
APressure increases proportionally
BPressure decreases (and vice versa)
CTemperature increases to compensate
DThe fluid density increases
Show Answer
✔ B — Pressure decreases (and vice versa)
Bernoulli's Principle: In streamline flow, the total mechanical energy (pressure + kinetic energy + potential energy) per unit volume is constant:
P + ½ρv² + ρgh = constant
Therefore: where velocity (v) is HIGH → pressure (P) is LOW; where velocity is LOW → pressure is HIGH.
Applications:
- Aeroplane lift: air moves faster over curved wing top → lower pressure → upward lift
- Carburetor: fuel mixing
- Spray guns/atomizers
- Magnus effect: spinning ball curves (cricket, football)
*Why A is wrong:* Pressure and speed are inversely related in Bernoulli's principle, not proportional.
*Why C is wrong:* Bernoulli's equation doesn't directly involve temperature for ideal fluids.
*Why D is wrong:* Ideal fluids are incompressible — density doesn't change.
P + ½ρv² + ρgh = constant
Therefore: where velocity (v) is HIGH → pressure (P) is LOW; where velocity is LOW → pressure is HIGH.
Applications:
- Aeroplane lift: air moves faster over curved wing top → lower pressure → upward lift
- Carburetor: fuel mixing
- Spray guns/atomizers
- Magnus effect: spinning ball curves (cricket, football)
*Why A is wrong:* Pressure and speed are inversely related in Bernoulli's principle, not proportional.
*Why C is wrong:* Bernoulli's equation doesn't directly involve temperature for ideal fluids.
*Why D is wrong:* Ideal fluids are incompressible — density doesn't change.