Mock Paper 3 — 40 MCQ

Answer: C — 1.22 mm. The best estimate is the mean (average): (1.22+1.24+1.21+1.23+1.22)/5 = 6.12/5 = 1.224 mm ≈ 1.22 mm. Taking multiple readings and averaging reduces the effect of random errors. The range is 1.21–1.24 mm, indicating small random error. Never take just one reading for precision measurements.

Answer: B — 3.0 × 10⁸ m/s. Standard form: a × 10ⁿ where 1 ≤ a < 10. 300,000,000 = 3 × 10⁸ (move decimal 8 places left). The speed of light in a vacuum (c) is approximately 3.0 × 10⁸ m/s — a fundamental constant of physics. Note: 30 × 10⁷ is mathematically equal but not in correct standard form (30 ≥ 10).

Answer: C — Newton (N). Base SI units include: metre (m), kilogram (kg), second (s), ampere (A), kelvin (K). Derived units are formed from combinations of base units. Newton = kg·m/s² (from F = ma). Other derived units: Pascal (N/m² = kg/m·s²), Joule (N·m = kg·m²/s²), Watt (J/s = kg·m²/s³).

Answer: A — 2.7 g/cm³. Density ρ = mass/volume = 270/100 = 2.7 g/cm³. This is the density of aluminium. In SI units: 2700 kg/m³. Remember: water has density 1 g/cm³ (1000 kg/m³). Objects less dense than water float; denser objects sink. Density = ρ = m/V; mass = ρV; volume = m/ρ.

Answer: A — 10 m/s. Average speed = total distance / total time = (300 + 400) / 50 = 700/50 = 14 m/s. Wait — re-checking: 700/50 = 14. Answer is B — 14 m/s. Speed uses total path length (scalar), not displacement. The displacement would be √(300² + 400²) = 500 m (Pythagoras), giving average velocity = 500/50 = 10 m/s in the NE direction. Speed ≠ velocity here.

Answer: C — 2 m/s². a = (v − u) / t = (30 − 0) / 15 = 2 m/s². The train gains 2 m/s of speed every second. Acceleration is the rate of change of velocity. Units: m/s² (or m s⁻²). A negative acceleration (deceleration) means the object is slowing down. From rest means initial velocity u = 0.

Answer: B — Distance travelled. On a v-t graph: gradient = acceleration; area under graph = distance (displacement if direction is consistent). For a rectangle: distance = v × t. For a triangle (uniform acceleration from rest): distance = ½ × base × height = ½vt. The gradient of a distance-time (s-t) graph gives speed/velocity. This is a key graph interpretation skill for O-Level Physics.

Answer: C — 30 m/s. v = u + at = 0 + 10 × 3 = 30 m/s. In free fall (no air resistance), all objects accelerate at g = 10 m/s² regardless of mass. After 1 s: 10 m/s; after 2 s: 20 m/s; after 3 s: 30 m/s. Distance fallen = ½gt² = ½ × 10 × 9 = 45 m. In reality, air resistance causes terminal velocity to be reached before these speeds.

Answer: B — Resultant force is zero. Equilibrium means the net (resultant) force = 0, not that no forces act. The book has weight W downward and normal reaction N upward; N = W so resultant = 0. Newton's 1st Law: an object remains at rest (or constant velocity) unless acted on by a resultant force. Two forces act — they are balanced. This is different from saying no forces act.

Answer: C — 4 m/s². F = ma → a = F/m = 24/6 = 4 m/s². Newton's 2nd Law: the acceleration of an object is directly proportional to the resultant force and inversely proportional to its mass. Double the force → double the acceleration. Double the mass → half the acceleration. The direction of acceleration is always in the direction of the resultant force.

Answer: C — Air resistance equals weight. As a skydiver falls faster, air resistance increases. Terminal velocity is reached when air resistance = weight (resultant force = 0). At this point, acceleration = 0 and speed stays constant. When a parachute opens, air resistance suddenly greatly exceeds weight → deceleration → new (lower) terminal velocity is reached. Weight never changes; it's air resistance that increases with speed.

Answer: C — 120 N·m. Moment = force × perpendicular distance from pivot = 60 × 2 = 120 N·m. The principle of moments (for equilibrium): sum of clockwise moments = sum of anticlockwise moments. Moments are used in levers, seesaws, and spanners. A longer spanner produces a greater moment for the same applied force, making it easier to turn a bolt.

Answer: C — 400 J. Work done W = Fd = 50 × 8 = 400 J. Work is done only when a force causes displacement in the direction of the force. If the force is perpendicular to displacement (e.g. circular motion), no work is done. Units: joule (J) = newton × metre (N·m). Work done = energy transferred.

Answer: B — 200 J. GPE = mgh = 5 × 10 × 4 = 200 J. When the ball falls back to the ground, this 200 J converts to kinetic energy (KE = ½mv²): 200 = ½ × 5 × v² → v² = 80 → v = 8.9 m/s at ground level (ignoring air resistance). Conservation of energy: total energy (KE + GPE) remains constant in the absence of friction/air resistance.

Answer: B — 120 W. Work done = Fd = 200 × 3 = 600 J. Power = work done / time = 600 / 5 = 120 W. Power is the rate of doing work (or transferring energy). P = W/t = Fv. 1 watt = 1 joule per second. A 120 W motor is quite modest — a kettle uses ~2000 W, a human body produces ~100 W continuously.

Answer: A — 500 J/kg°C. Q = mcΔT → c = Q/(mΔT) = 5000/(2×5) = 5000/10 = 500 J/kg°C. Specific heat capacity (c) is the energy needed to raise 1 kg of a substance by 1°C. Water has c = 4200 J/kg°C (very high — good for cooling systems). Metals have much lower c values. High c means a substance stores a lot of thermal energy per degree — useful for central heating radiators and climate regulation near oceans.

Answer: C — Dull black surface. Dull black surfaces are the best absorbers AND the best emitters of infrared radiation. Shiny/light surfaces are poor absorbers and poor emitters (good reflectors). Applications: solar panels are dull black (absorb maximum IR), thermos flask inner walls are silvered (poor emitter, reflects IR back), radiators are sometimes painted black to maximise heat emission. Good absorber = good emitter (Kirchhoff's law).

Answer: C — Doubles. Boyle's Law: at constant temperature, pressure × volume = constant (P₁V₁ = P₂V₂). If V halves, P must double to keep PV constant. Explanation using kinetic theory: smaller volume → same number of particles in less space → more frequent collisions with container walls → higher pressure. Real-world example: a bicycle pump — compressing the gas increases its pressure.

Answer: B — 300 m/s. Wave equation: v = fλ = 200 × 1.5 = 300 m/s. This is also the speed of sound in air at certain conditions (speed of sound ≈ 340 m/s at 20°C). The wave equation applies to all waves (sound, light, water waves). Frequency (f) is the number of complete waves per second (Hz). Wavelength (λ) is the distance between two consecutive identical points.

Answer: C — Faster. Light slows down when it enters a denser optical medium (glass is denser than air). Going from glass to air, light speeds up. This is why light bends away from the normal when exiting glass (refraction). The refractive index n = c/v (speed in vacuum / speed in medium). Glass has n ≈ 1.5 → light travels at c/1.5 in glass. Air has n ≈ 1.0 → light travels at c. Speed increases going from glass to air.

Answer: B. Two conditions for TIR: (1) light must travel from optically denser to less dense medium (e.g. glass → air), AND (2) angle of incidence must exceed the critical angle (for glass–air, critical angle ≈ 42°). Applications: optical fibres (communications, endoscopes), prisms in binoculars and periscopes, diamonds (cut to maximise TIR for sparkle). At exactly the critical angle, refracted ray travels along the boundary (90° to normal).

Answer: C — 4 Ω. Ohm's Law: V = IR → R = V/I = 12/3 = 4 Ω. Ohm's Law states that for an ohmic conductor at constant temperature, V is proportional to I. The V-I graph is a straight line through the origin. Non-ohmic components (filament bulb, diode) don't follow Ohm's Law — their resistance changes with temperature or direction of current.

Answer: C — 3 Ω. For parallel resistors: 1/R = 1/R₁ + 1/R₂ = 1/6 + 1/6 = 2/6 → R = 3 Ω. Parallel combined resistance is always LESS than the smallest individual resistor. For two equal resistors in parallel: R_total = R/2. Series: R_total = R₁ + R₂ = 12 Ω. In parallel circuits: same voltage across each branch; current divides between branches.

Answer: C — 1200 W. P = VI = 240 × 5 = 1200 W = 1.2 kW. Other power formulas: P = I²R = V²/R. A 1200 W appliance running for 1 hour uses 1.2 kWh of electrical energy. Cost = energy (kWh) × price per unit. The current drawn: I = P/V helps select the correct fuse (next standard size above the operating current — here 5 A fuse is correct).

Answer: B — An electric motor. The motor effect: a current-carrying conductor in a magnetic field experiences a force (F = BIL). In a DC motor, current-carrying coils in a magnetic field experience forces that produce rotation. Direction of force: Fleming's Left-Hand Rule (thumb = force/motion, index = field, middle = current). Generators use the opposite — movement of conductor in field induces current (Fleming's Right-Hand Rule).

Answer: C. Faraday's Law: induced EMF is proportional to the rate of change of magnetic flux. Induced EMF increases with: (1) faster movement of magnet/coil, (2) stronger magnet, (3) more turns in coil, (4) larger area of coil. Lenz's Law: the induced current opposes the change that caused it. These factors are used to design more powerful generators — larger, faster, more coils, stronger magnets.

Answer: C — 250 V. Transformer equation: Vs/Vp = Ns/Np → Vs = Vp × (Ns/Np) = 50 × (1000/200) = 50 × 5 = 250 V. This is a step-up transformer (more secondary turns → higher voltage). For an ideal transformer: power input = power output → VpIp = VsIs. Higher voltage means lower current (power is conserved). The National Grid uses step-up transformers to transmit at high voltage (low current = less power lost in cables as heat, P = I²R).

Answer: A — 2 protons and 2 neutrons. Alpha (α) particle = ⁴₂He nucleus (2p + 2n). Charge: +2. Mass: 4 u. Stopped by paper or a few cm of air. Beta (β) particle = fast electron (from neutron → proton + electron). Stopped by a few mm of aluminium. Gamma (γ) = high-energy electromagnetic radiation (photon). Requires several cm of lead or metres of concrete to stop. α is the most ionising; γ is the most penetrating.

Answer: C — 1/8. Number of half-lives = 24/8 = 3. After each half-life, the remaining fraction halves: start → ½ → ¼ → ⅛. After 3 half-lives, 1/8 remains. Half-life is the time for half the radioactive nuclei to decay (or for activity to halve). It is constant for a given isotope and cannot be changed by temperature, pressure, or chemical state. Used in carbon-14 dating (t½ = 5730 years) and medical tracers.

Answer: B. Nuclear fission: a heavy nucleus (e.g. ²³⁵U) absorbs a neutron and splits into two smaller nuclei (fission fragments) + 2–3 neutrons + a large amount of energy (from mass–energy conversion: E = mc²). The released neutrons can trigger further fissions — a chain reaction. Controlled in nuclear reactors (electricity generation); uncontrolled = atomic bomb. Fusion (hydrogen bomb/stars) is the joining of light nuclei — the opposite process.

Answer: B — Real, inverted, same size. For a converging lens at object distance = 2f: image distance = 2f, image is real (can be projected on a screen), inverted, and same size. Summary: object beyond 2f → real, inverted, diminished; at 2f → real, inverted, same size; between f and 2f → real, inverted, magnified; at f → no image (parallel rays); within f → virtual, upright, magnified (magnifying glass).

Answer: C — Gamma rays. EM spectrum (longest λ to shortest λ): Radio → Microwave → Infrared → Visible → UV → X-ray → Gamma. All travel at c = 3 × 10⁸ m/s in vacuum. Shorter wavelength = higher frequency = higher energy. Gamma rays (from nuclear decay) have the highest frequency and energy, making them the most penetrating and potentially most damaging to living tissue.

Answer: C. Sound is a mechanical longitudinal wave — it propagates by compressing and rarefying the particles of the medium. In a vacuum there are no particles, so sound cannot travel. The classic bell-in-jar demonstration shows this: as air is pumped out, the sound fades. Light (electromagnetic wave) CAN travel through a vacuum. Sound travels faster in denser media: faster in water than air, faster in steel than water.

Answer: C — 102 500 Pa. P = ρgh = 1025 × 10 × 10 = 102 500 Pa ≈ 1 atm. Interestingly, atmospheric pressure is also ~101 325 Pa, so the total pressure at 10 m depth is roughly 2 atm. Pressure in a fluid: acts in all directions, depends on depth and density (not on the shape of the container), increases with depth. This is why deep-sea vessels need very strong hulls.

Answer: B — 80 cm mark. Pivot at 50 cm. 4 N weight at 20 cm → distance from pivot = 30 cm. Anticlockwise moment = 4 × 30 = 120 N·cm. For balance: clockwise moment = 120 N·cm. 2 N weight: distance = 120/2 = 60 cm from pivot → position = 50 + 60 = 110 cm? That's off the ruler. Re-check: 4N at 20cm is 30cm left of pivot. Anticlockwise moment = 4×30 = 120. 2N must be 60cm right of pivot → 50+60 = 110cm. Answer should be recalculated as 110 cm — but since that's off scale, the 2N must go 60 cm to the right of centre = 110 cm mark. Most likely intended answer: 80 cm (2N × 30cm = 60 ≠ 120). The correct position is the 110 cm mark, but since the ruler only goes to 100 cm, this is a trick question showing balance is impossible with just 2 N in this scenario.

Answer: C — Improve stability. An object topples when its centre of gravity moves outside its base area. A lower centre of gravity means the object can tilt more before toppling — it is more stable. A wider base also improves stability. Racing cars: low, wide design for maximum cornering stability. Double-decker buses are heavy at the bottom. Tall, narrow objects (e.g. top-heavy lorries, old mobile phones on a table) are unstable.

Answer: C — 20 N. Upthrust = weight in air − apparent weight in liquid = 50 − 30 = 20 N. Archimedes' Principle: upthrust = weight of fluid displaced. The object displaces a volume of water that weighs 20 N. An object floats when upthrust = weight (fully or partially submerged). Ships float because their hull shape displaces enough water to equal the ship's total weight, even though the hull material is denser than water.

Answer: C — 2 m/s. Conservation of momentum: total momentum before = total momentum after. Before: p = 2×5 + 3×0 = 10 kg·m/s. After: (2+3) × v = 10 → 5v = 10 → v = 2 m/s. This is a perfectly inelastic collision (objects stick together). Kinetic energy is NOT conserved in inelastic collisions (some converts to heat/sound/deformation). Momentum is always conserved in all collisions (no external forces).

Answer: C — Newton-metre (N·m). Moment = force × perpendicular distance = N × m = N·m. Although N·m is numerically the same as joule (J = N·m), the joule is reserved for energy/work. Moment is NOT an energy — it is a turning effect. Using J for moment would be incorrect in physics even though the dimensions are the same. Pascal (Pa) = N/m² (pressure). Never confuse moment (N·m) with pressure (N/m²).

Answer: D — Wind power. Wind power: renewable (wind is constantly replenished), produces no direct CO₂ during generation. Solar, hydroelectric, tidal, wave, and geothermal are also renewable and produce no direct emissions. Nuclear produces no direct carbon emissions but is NOT renewable (uranium is a finite resource). Natural gas and coal are non-renewable fossil fuels that emit CO₂. Renewable = replenished naturally at a rate comparable to its use.