Practice igcse model questions vol1 physics 2020 Past Questions

Question 1 View Details

A block of mass \(5.0\) kg rests on a rough inclined plane that makes an angle of \(30^{\circ}\) with the horizontal. It is pulled up the plane by a horizontal force of magnitude \(F\). The coefficient of kinetic friction between the block and the plane is \(\mu = 0.20\). The block moves up the plane with constant speed. Determine the magnitude of the horizontal force \(F\) (in newtons) required to keep the block moving at constant speed.

A. 30 N

B. 50 N

C. 38 N

Correct D. 43 N

Correct Answer: D

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Question 2 View Details

A sample initially contains \(2.0\times10^{6}\) atoms of a radioactive isotope \(A\). Isotope \(A\) decays to isotope \(B\) with a half‑life of \(30\) min, and isotope \(B\) subsequently decays to a stable isotope \(C\) with a half‑life of \(10\) min. No atoms of \(B\) are present initially. After \(40\) min the total activity of the sample (decays per second from both \(A\) and \(B\)) is measured. Calculate the activity of the sample at that time, giving your answer in becquerels (Bq).

A. 800 Bq

B. 600 Bq

C. 500 Bq

Correct D. 692 Bq

Correct Answer: D

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Question 3 View Details

A block of mass \(4.0\) kg rests on a smooth incline that makes an angle of \(20^{\circ}\) with the horizontal. It is attached by a light string over a frictionless pulley to a hanging mass \(m_2=5.0\) kg. The coefficient of kinetic friction between the block and the incline is \(\mu = 0.25\). The system is released from rest. Determine (a) the magnitude of the acceleration of the system (in \(\text{m s}^{-2}\)) and (b) the tension in the string (in newtons).

Correct A. 2.9 m/s^2; 34 N

B. 4.2 m\/s^2; 50 N

C. 1.8 m\/s^2; 20 N

D. 3.5 m\/s^2; 40 N

Correct Answer: A

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Question 4 View Details

A string of length \(1.20\) m and linear mass density \(8.0\times10^{-3}\) kg m\(^{-1}\) is fixed at both ends and is under an unknown tension \(T\). The string vibrates in its third harmonic and the observed frequency is \(120\) Hz. Determine the tension \(T\) in newtons.

A. 90 N

B. 82 N

C. 68 N

Correct D. 74 N

Correct Answer: D

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Question 5 View Details

A police car equipped with a siren that emits a frequency of \(800\) Hz moves directly towards a stationary observer at a speed of \(30\) m s\(^{-1}\). At the same time the observer is walking away from the car at \(5\) m s\(^{-1}\). The speed of sound in air is \(340\) m s\(^{-1}\). What frequency does the observer hear? Give your answer to the nearest hertz.

Correct A. 865 Hz

B. 724 Hz

C. 890 Hz

D. 877 Hz

Correct Answer: A

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Question 6 View Details

The diagram shows an inclined plane of length \(4.0\) m making an angle of \(30^{\circ}\) with the horizontal. A block of mass \(1.5\) kg is attached to a spring of constant \(300\) N m\(^{-1}\) fixed at the top of the incline. The spring is compressed by \(0.20\) m when the block is held at the top and then released. The surface is frictionless. \(\text{(i)}\) Calculate the speed of the block when it reaches the bottom of the incline. \(\text{(ii)}\) Assuming the block travels the whole length of the incline, find the average power delivered by the spring during the motion.

Correct A. Speed \(=6.9\) m s\(^{-1}\); average power \(=5.2\) W

B. Speed \(=6.2\) m s\(^{-1}\); average power \(=5.9\) W

C. Speed \(=5.8\) m s\(^{-1}\); average power \(=4.1\) W

D. Speed \(=7.4\) m s\(^{-1}\); average power \(=6.8\) W

Correct Answer: A

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Question 7 View Details

In the laboratory setup shown, a metal cylinder is weighed on a balance (mass \(120\) g). It is then placed gently into a measuring cylinder containing water. The water level rises from \(30.0\) mL to \(45.0\) mL. Assuming the water density is \(1.0\) g cm\(^{-3}\), determine the density of the metal cylinder in \(\text{kg m}^{-3}\).

A. 7.2×10³ kg m⁻³

B. 6.0×10³ kg m⁻³

C. 9.5×10³ kg m⁻³

Correct D. 8.0×10³ kg m⁻³

Correct Answer: D

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Question 8 View Details

A sealed container holds \(2.00\) mol of an ideal gas at \(300\) K and a pressure of \(1.00\times10^{5}\) Pa. The gas is heated at constant volume to \(450\) K. It then expands isothermally at \(450\) K until the pressure returns to \(1.00\times10^{5}\) Pa. What is the final volume of the gas after the expansion? Give your answer in \(\text{m}^{3}\) to two significant figures.

A. 6.0×10⁻² m³

Correct B. 7.5×10⁻² m³

C. 5.5×10⁻² m³

D. 8.2×10⁻² m³

Correct Answer: B

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Question 9 View Details

Two quantities of water are mixed in an insulated container. \(200\) g of water at \(80^{\circ}\)C is mixed with \(300\) g of water at \(20^{\circ}\)C. The specific heat capacity of water is \(4.18\) J g\(^{-1}\)K\(^{-1}\). Assuming no heat loss to the surroundings, calculate the final equilibrium temperature of the mixture in degrees Celsius.

A. 38 °C

B. 62 °C

Correct C. 44 °C

D. 50 °C

Correct Answer: C

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Question 10 View Details

A spectral line of wavelength \(434\) nm is observed in the emission spectrum of hydrogen. Assuming the line belongs to the Balmer series (final level \(n_f=2\)), determine the initial energy level \(n_i\) of the transition. Then calculate the energy of the emitted photon in joules. Use the Rydberg constant \(R=1.097\times10^{7}\) m\(^{-1}\), Planck's constant \(h=6.626\times10^{-34}\) J s and the speed of light \(c=3.00\times10^{8}\) m s\(^{-1}\).

A. Transition \(n_i=6\)→2; photon energy \(≈4.9×10^{-19}\) J

B. Transition \(n_i=3\)→2; photon energy \(≈3.0×10^{-19}\) J

C. Transition \(n_i=4\)→2; photon energy \(≈4.1×10^{-19}\) J

Correct D. Transition \(n_i=5\)→2; photon energy \(≈4.6×10^{-19}\) J

Correct Answer: D

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Question 11 View Details

A car travels at a speed of \(90\ \text{km h}^{-1}\). If it moves for \(45\) minutes, what distance does it cover in metres?

A. 40500

B. 6750

Correct C. 67500

D. 4050000

Correct Answer: C

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Question 12 View Details

A converging lens forms a real image on a screen that is \(50\) cm away from the object. The image is three times taller than the object. Determine the focal length of the lens in centimetres (give your answer to one decimal place).

A. 12.5

B. 9.3

C. 37.5

Correct D. 9.4

Correct Answer: D

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Question 13 View Details

A string fixed at both ends has a fundamental frequency of \(50\) Hz when the tension in the string is \(T\). The tension is increased so that the frequency of the fourth harmonic becomes \(260\) Hz. By what factor is the new tension greater than the original tension? Give your answer to two decimal places.

A. 2.00

B. 1.85

Correct C. 1.69

D. 1.58

Correct Answer: C

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Question 14 View Details

A block‑and‑tackle system lifts a load of \(200\) N through a vertical distance of \(0.5\) m in \(2\) s. The effort applied moves through \(2.5\) m with a constant force of \(80\) N. Calculate the efficiency of the system (as a percentage) and the power output in watts.

A. 40% and 40 W

Correct B. 50% and 50 W

C. 55% and 55 W

D. 60% and 60 W

Correct Answer: B

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Question 15 View Details

A metal block has a mass of \(2.5\) kg and a volume of \(0.0012\) m\(^3\). Determine its density in grams per cubic centimetre, giving your answer to one decimal place.

A. 1.8

B. 2.3

C. 2.0

Correct D. 2.1

Correct Answer: D

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Question 16 View Details

A block and tackle system consists of a fixed pulley and a movable pulley used to lift a load of 500 \(\text{N}\). The effort rope is pulled through a distance of 2.0 \(\text{m}\) while the load rises 0.8 \(\text{m}\). The axle of the movable pulley has a frictional torque of 2.0 \(\text{N·m}\) and its radius is 0.05 \(\text{m}\). (a) Calculate the ideal mechanical advantage (IMA). (b) Determine the actual mechanical advantage (AMA). (c) Find the efficiency of the system as a percentage.

A. IMA = 2.5, AMA ≈ 2.0, efficiency ≈ 80 %

Correct B. IMA = 2.5, AMA ≈ 1.72, efficiency ≈ 69 %

C. IMA = 3.0, AMA ≈ 2.1, efficiency ≈ 70 %

D. IMA = 2.0, AMA ≈ 1.5, efficiency ≈ 55 %

Correct Answer: B

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Question 17 View Details

A boat sails 30 \(\text{km}\) due north and then 40 \(\text{km}\) due east. Find the magnitude of the resultant displacement and the direction measured east of north.

A. 70 \\((\\text{km}\\) and 45° east of north

B. 55 \\((\\text{km}\\) and 30° east of north

Correct C. 50 \(\text{km}\) and 53.1° east of north

D. 40 \\((\\text{km}\\) and 60° east of north

Correct Answer: C

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Question 18 View Details

A 200 \(\text{g}\) metal piece at 150°C is placed into 500 \(\text{g}\) of water at 20°C in an insulated container. After equilibrium the temperature is 30°C. (a) Determine the specific heat capacity of the metal (in J g⁻¹°C⁻¹) assuming no heat is lost to the container. (b) If 5% of the heat transferred from the metal to the water is lost to the container, recalculate the specific heat capacity.

A. a) 0.75 J g⁻¹°C⁻¹, b) 0.80 J g⁻¹°C⁻¹

B. a) 0.95 J g⁻¹°C⁻¹, b) 1.00 J g⁻¹°C⁻¹

Correct C. a) 0.87 J g⁻¹°C⁻¹, b) 0.92 J g⁻¹°C⁻¹

D. a) 0.65 J g⁻¹°C⁻¹, b) 0.70 J g⁻¹°C⁻¹

Correct Answer: C

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Question 19 View Details

A circuit consists of a 12 V battery with internal resistance \(r\) connected to a lamp of resistance 4 \(\Omega\) in series with a parallel combination of a 6 \(\Omega\) resistor and a 3 \(\Omega\) resistor. The lamp is rated at 6 W when operating at its normal voltage. (a) Determine the internal resistance \(r\) of the battery. (b) Find the current through the lamp. (c) State the terminal voltage across the lamp.

A. a) r ≈ 2.5 Ω, b) I ≈ 1.50 A, c) V_lamp ≈ 5.5 V

B. a) r ≈ 3.0 Ω, b) I ≈ 1.30 A, c) V_lamp ≈ 5.0 V

C. a) r ≈ 4.5 Ω, b) I ≈ 1.10 A, c) V_lamp ≈ 4.4 V

Correct D. a) r ≈ 3.8 Ω, b) I ≈ 1.23 A, c) V_lamp ≈ 4.9 V

Correct Answer: D

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Question 20 View Details

A source emits sound of frequency 500 Hz. The source moves towards a stationary observer at 20 m s⁻¹ while the observer moves away from the source at 10 m s⁻¹. The speed of sound in air is 340 m s⁻¹. (a) Calculate the frequency heard by the observer. (b) If the observed frequency is measured as 540 Hz under the same motions, determine the actual speed of sound in the air.

A. a) ≈ 500 Hz, b) v ≈ 300 m s⁻¹

B. a) ≈ 540 Hz, b) v ≈ 200 m s⁻¹

Correct C. a) ≈ 516 Hz, b) v ≈ 145 m s⁻¹

D. a) ≈ 530 Hz, b) v ≈ 350 m s⁻¹

Correct Answer: C

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Question 21 View Details

A rectangular steel block has dimensions 10 cm \(\times\) 8 cm \(\times\) 5 cm. Its density is \(7800 \text{ kg m}^{-3}\) and its specific heat capacity is \(470 \text{ J kg}^{-1}\!\,^{\circ}\!\text{C}^{-1}\). A heating coil supplies \(5000 \text{ J}\) of energy, but 20% of this energy is lost to the surroundings. If the block starts at \(20^{\circ}\!\text{C}\), what is its final temperature (to one decimal place)?

Correct A. 22.7 \(^\circ\)C

B. 26.3 \(^\circ\)C

C. 20.5 \(^\circ\)C

D. 24.1 \(^\circ\)C

Correct Answer: A

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Question 22 View Details

A fixed point charge \(Q = +8 \;\mu\text{C}\) is located at the origin. A small sphere of mass \(0.010 \text{ kg}\) and charge \(q = -2 \;\mu\text{C}\) is released from rest at point \(A(0.20\text{ m}, 0)\). It moves under the electrostatic force only to point \(B(0, 0.10\text{ m})\) where it momentarily stops after compressing a spring attached to a wall. Find the speed of the sphere just before it contacts the spring (i.e. at point \(B\)). Use \(k = 9.0 \times 10^{9} \text{ N m}^2\!\,\text{C}^{-2}\).

A. 8 \text{ m s}^{-1}

B. 14 \text{ m s}^{-1}

C. 10 \text{ m s}^{-1}

Correct D. 12 \text{ m s}^{-1}

Correct Answer: D

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Question 23 View Details

A car travels a total distance of \(200 \text{ m}\) in \(20 \text{ s}\). It starts from rest, accelerates uniformly for \(4 \text{ s}\), then moves at a constant speed, and finally decelerates uniformly to rest in \(6 \text{ s}\). Determine the maximum speed attained by the car (in \(\text{m s}^{-1}\), to two significant figures).

A. 11.8 \text{ m s}^{-1}

B. 15.0 \text{ m s}^{-1}

Correct C. 13.3 \text{ m s}^{-1}

D. 12.0 \text{ m s}^{-1}

Correct Answer: C

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Question 24 View Details

A block of mass \(1.5 \text{ kg}\) slides down a smooth incline that is \(4.0 \text{ m}\) long and makes an angle of \(25^{\circ}\) with the horizontal. At the bottom it encounters a rough horizontal surface (coefficient of kinetic friction \(\mu_k = 0.15\)) and, after travelling a total of \(1.2 \text{ m}\) on this surface, compresses a spring of constant \(k = 300 \text{ N m}^{-1}\) fixed to a wall and momentarily comes to rest. Find the maximum compression of the spring (in metres, to two decimal places).

A. 0.45 \text{ m}

B. 0.28 \text{ m}

Correct C. 0.39 \text{ m}

D. 0.32 \text{ m}

Correct Answer: C

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Question 25 View Details

An electric kettle rated at \(2.0 \text{ kW}\) is used to heat \(0.5 \text{ kg}\) of water from \(20^{\circ}\!\text{C}\) to its boiling point \(100^{\circ}\!\text{C}\). The kettle's efficiency is \(70\%\). After the water reaches \(100^{\circ}\!\text{C}\) the kettle is switched off and the water cools in a room at \(20^{\circ}\!\text{C}\). The rate of heat loss is proportional to the temperature difference with a constant of proportionality \(5 \text{ W}\!\,^{\circ}\!\text{C}^{-1}\).\n(a) How long does it take to bring the water to the boiling point?\n(b) How long does it take for the water to cool from \(100^{\circ}\!\text{C}\) to \(40^{\circ}\!\text{C}\)? Give your answer for (b) in seconds to three significant figures.

Correct A. 120 s (a); 5.80×10^2 s (b)

B. 110 s (a); 5.00×10^2 s (b)

C. 140 s (a); 4.80×10^2 s (b)

D. 130 s (a); 6.20×10^2 s (b)

Correct Answer: A

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