Practice igcse model questions vol1 physics 2023 Past Questions

Question 1 View Details

A car starts from rest, accelerates uniformly at \(2.0\ \text{m s}^{-2}\) for \(5.0\ \text{s}\), then moves at a constant speed for an unknown time, and finally decelerates uniformly to rest with a deceleration of \(3.0\ \text{m s}^{-2}\). The total distance travelled is \(500\ \text{m}\). Calculate the time (in seconds) the car spends travelling at constant speed. Give your answer to one decimal place.

A. 52.3

Correct B. 45.8

C. 40.2

D. 38.7

Correct Answer: B

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Question 2 View Details

A rectangular coil of \(N = 200\) turns rotates in a uniform magnetic field of magnitude \(B = 0.10\ \text{T}\). The coil has an area of \(A = 0.020\ \text{m}^2\) and rotates at a frequency of \(f = 50\ \text{Hz}\). The resistance of the coil itself is \(5.0\ \Omega\). The coil is connected to an external load resistor \(R_L\).\n\n(a) Determine the value of \(R_L\) that will allow the maximum average power to be delivered to the load.\n(b) Calculate that maximum average power (in watts), giving your answer to three significant figures.

Correct A. R_L = 5.0 Ω, P_max = 395 W

B. R_L = 10.0 Ω, P_max = 395 W

C. R_L = 5.0 Ω, P_max = 300 W

D. R_L = 2.5 Ω, P_max = 210 W

Correct Answer: A

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Question 3 View Details

Two forces act on an object in the same plane. Force \(\mathbf{F}_1\) has a magnitude of \(30\ \text{N}\) and is directed along the positive x‑axis. Force \(\mathbf{F}_2\) has a magnitude of \(40\ \text{N}\) and makes an angle of \(120^{\circ}\) measured counter‑clockwise from the positive x‑axis. Find the magnitude of the resultant force, giving your answer to one decimal place.

A. 34.5

B. 41.0

C. 38.2

Correct D. 36.1

Correct Answer: D

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Question 4 View Details

A stretched string of length \(L = 0.80\ \text{m}\) is fixed at both ends. Its linear mass density is \(\mu = 5.0 \times 10^{-3}\ \text{kg m}^{-1}\). The string vibrates in its fundamental mode with a frequency of \(f = 120\ \text{Hz}\). Determine the tension in the string (in newtons), giving your answer to three significant figures.

A. 170

Correct B. 184

C. 200

D. 150

Correct Answer: B

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Question 5 View Details

A point charge \(Q = +8.0\ \mu\text{C}\) is fixed at the origin of an x‑axis. A second charge \(q = -2.0\ \mu\text{C}\) is placed on the same axis at \(x = 0.12\ \text{m}\). At what position \(x\) (in meters, measured from the origin) on the axis is the net electric field zero? Give your answer to two decimal places.

Correct A. 0.08

B. 0.04

C. 0.16

D. 0.10

Correct Answer: A

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Question 6 View Details

An ideal gas is contained in a sealed vessel at an initial pressure of 150 kPa, volume 2.00 L and temperature 300 K. The gas is heated to 350 K while the vessel is allowed to expand until the pressure returns to its original value of 150 kPa. The gas is then heated further to 400 K while the volume is kept constant at the value reached after the first heating. What is the final pressure of the gas (in kPa)?

Correct A. 171 kPa

B. 150 kPa

C. 160 kPa

D. 190 kPa

Correct Answer: A

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Question 7 View Details

A string 1.20 m long is fixed at both ends. Its linear mass density is \(5.0\times10^{-3}\ \text{kg m}^{-1}\). Initially a mass of 0.80 kg hangs from the string, providing the tension. The string vibrates in its fundamental mode. The source frequency is then increased by 20 % while an additional 0.20 kg mass is added to the hanging weight. What is the wavelength (in metres, to two decimal places) of the wave travelling in the string after these changes?

A. 2.00 m

B. 1.96 m

C. 2.48 m

Correct D. 2.24 m

Correct Answer: D

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Question 8 View Details

An isolated conducting sphere of radius \(R = 0.040\ \text{m}\) is initially uncharged. A point charge \(+Q = 8.0\ \mu\text{C}\) is placed on the axis at a distance \(a = 0.10\ \text{m}\) to the right of the sphere's centre. The sphere is then grounded, allowing charge to flow. Determine the magnitude of the electric field at point \(P\) located \(0.20\ \text{m}\) to the left of the sphere's centre (on the same axis). Give your answer in scientific notation to two significant figures, and state the direction (towards the left or right).

Correct A. 1.8×10^5 N/C leftwards

B. 2.3×10^5 N\/C leftwards

C. 1.2×10^5 N\/C leftwards

D. 1.8×10^5 N\/C rightwards

Correct Answer: A

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Question 9 View Details

An acoustic source emits a tone of frequency \(f = 500\ \text{Hz}\). The source moves directly towards a stationary observer at a speed of \(10\ \text{m s}^{-1}\). The speed of sound in air is \(340\ \text{m s}^{-1}\). (a) What frequency does the observer initially hear? (b) If the observer then starts moving directly away from the source at \(5\ \text{m s}^{-1}\) while the source continues its motion, what frequency does the observer hear now? Give your answers to the nearest whole hertz.

A. 520 Hz, 503 Hz

B. 510 Hz, 500 Hz

Correct C. 515 Hz, 508 Hz

D. 525 Hz, 495 Hz

Correct Answer: C

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Question 10 View Details

An ion of singly ionised helium (He\(^+\)) has nuclear charge \(Z = 2\). An electron in this ion drops from the \(n = 4\) level to the \(n = 2\) level, emitting a photon. (a) Calculate the energy of the photon in joules (to three significant figures). (b) Determine the wavelength of the emitted radiation in nanometres (to three significant figures). (c) State whether the radiation lies within the visible spectrum (400-700 nm).

Correct A. 1.63×10^-18 J; 122 nm; not visible

B. 1.63×10^-18 J; 130 nm; not visible

C. 1.70×10^-18 J; 115 nm; not visible

D. 1.63×10^-18 J; 122 nm; visible

Correct Answer: A

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Question 11 View Details

A long solenoid \(0.50\ \text{m}\) long has \(800\) turns and carries a current \(I\). A straight horizontal wire \(10\ \text{cm}\) long carrying a current of \(2.0\ \text{A}\) is placed at the centre of the solenoid, perpendicular to the solenoid's magnetic field. The wire has a mass of \(20\ \text{g}\). Determine the current \(I\) (in amperes, to the nearest ampere) required so that the magnetic force on the wire equals its weight.

A. 610 A

Correct B. 488 A

C. 525 A

D. 452 A

Correct Answer: B

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Question 12 View Details

A \(10.0\ \text{L}\) container holds \(2.0\ \text{mol}\) of an ideal gas at \(300\ \text{K}\). The gas is heated at constant volume until its pressure doubles. It then expands adiabatically (\(\gamma = 1.4\)) until the temperature returns to \(300\ \text{K}\). Calculate the final volume of the gas (in litres, to three significant figures).

A. 1.90 L

B. 1.55 L

C. 2.00 L

Correct D. 1.77 L

Correct Answer: D

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Question 13 View Details

A \(250\ \text{g}\) copper block (specific heat \(c_{Cu}=0.385\ \text{J g}^{-1}\text{K}^{-1}\)) initially at \(150\ ^\circ\text{C}\) is placed into \(100\ \text{g}\) of water (specific heat \(c_{w}=4.18\ \text{J g}^{-1}\text{K}^{-1}\)) initially at \(20\ ^\circ\text{C}\) in an insulated container. After equilibrium the temperature of the system is \(30\ ^\circ\text{C}\). What percentage of the heat lost by the copper is transferred to the water? Give your answer to one decimal place.

Correct A. 36.2 %

B. 33.1 %

C. 28.7 %

D. 40.5 %

Correct Answer: A

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Question 14 View Details

A bimetallic strip consists of two metals of equal thickness bonded together. Each metal is \(100\ \text{mm}\) long at \(20\ ^\circ\text{C}\). The coefficients of linear expansion are \(\alpha_A = 12\times10^{-6}\ \text{°C}^{-1}\) and \(\alpha_B = 20\times10^{-6}\ \text{°C}^{-1}\). When heated uniformly the strip bends into an arc whose radius of curvature (measured to the neutral axis midway through the thickness) is \(500\ \text{mm}\). If the total thickness of the strip is \(2.0\ \text{mm}\), determine the temperature increase \(\Delta T\) (in °C) that produced this curvature. Give your answer as an integer.

A. 350

Correct B. 500

C. 450

D. 600

Correct Answer: B

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Question 15 View Details

A \(12\ \text{V}\) battery with internal resistance \(r\) supplies a circuit containing two resistors, \(R_1 = 4\ \Omega\) and an unknown \(R_2\), connected in parallel. The total current drawn from the battery is \(3.0\ \text{A}\). When a second identical \(12\ \text{V}\) battery (same internal resistance \(r\)) is connected in series with the first, the total current rises to \(4.5\ \text{A}\). Determine the values of \(R_2\) (in \(\Omega\), to the nearest whole number) and the internal resistance \(r\) (in \(\Omega\), to two decimal places).

A. R2 = 8 Ω, r = 1.00 Ω

B. R2 = 10 Ω, r = 1.50 Ω

C. R2 = 6 Ω, r = 1.33 Ω

Correct D. R2 = 8 Ω, r = 1.33 Ω

Correct Answer: D

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Question 16 View Details

A sealed cylinder contains \(0.5\ \text{mol}\) of an ideal gas at a temperature of \(300\ \text{K}\) and a pressure of \(150\ \text{kPa}\). The gas is first compressed isothermally until its volume is reduced to half its original value. It is then heated at constant volume until the pressure rises to \(450\ \text{kPa}\). What is the final temperature of the gas in kelvin? Give your answer to the nearest kelvin.

A. 500

Correct B. 450

C. 300

D. 600

Correct Answer: B

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Question 17 View Details

A car starts from rest and accelerates uniformly for \(20\ \text{s}\). It then travels at a constant speed for a period of time, and finally decelerates uniformly to rest in \(10\ \text{s}\), reaching its destination B. The total time taken for the whole journey is \(70\ \text{s}\) and the total distance covered is \(1800\ \text{m}\). What is the constant speed (in \(\text{m\,s}^{-1}\)) during the middle part of the journey? Give your answer to two decimal places.

A. 28.45

B. 35.50

Correct C. 32.73

D. 30.00

Correct Answer: C

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Question 18 View Details

A person walks \(5.0\ \text{km}\) due north and then walks \(12.0\ \text{km}\) at an angle of \(30^{\circ}\) east of north. Determine the magnitude of the resultant displacement in kilometres (to two decimal places) and state its direction as an angle east of north (to one decimal place).

A. 18.03 km, 27.5° east of north

B. 13.45 km, 15.8° east of north

Correct C. 16.52 km, 21.0° east of north

D. 14.90 km, 19.2° east of north

Correct Answer: C

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Question 19 View Details

A runner completes a \(5.0\ \text{km}\) race in \(21\) minutes and \(30\) seconds. Calculate the runner's average speed in metres per second, correct to two decimal places.

A. 3.20

B. 3.45

Correct C. 3.88

D. 4.12

Correct Answer: C

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Question 20 View Details

A block of mass \(8.0\ \text{kg}\) rests on a horizontal rough surface. It is pulled by a rope that makes an angle of \(30^{\circ}\) above the horizontal with a tension \(T\). The coefficient of static friction between the block and the surface is \(0.40\). The block is just about to move. Determine the minimum tension \(T\) (in newtons) required to start the motion. Give your answer to two decimal places.

A. 34.64

Correct B. 29.41

C. 24.00

D. 26.53

Correct Answer: B

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Question 21 View Details

A converging lens forms a real image on a screen \(12\ \text{cm}\) from the lens. The image is three times larger than the object. Determine the object distance and the focal length of the lens.

A. object distance = 3 cm, focal length = 4 cm

B. object distance = 5 cm, focal length = 2.5 cm

C. object distance = 6 cm, focal length = 2 cm

Correct D. object distance = 4 cm, focal length = 3 cm

Correct Answer: D

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Question 22 View Details

A \(5.0\ \text{kg}\) block rests on a rough inclined plane that makes an angle of \(30^{\circ}\) with the horizontal. The block is held in equilibrium by a rope that pulls parallel to the plane upward. The tension in the rope is \(20\ \text{N}\). Determine the coefficient of static friction between the block and the plane.

A. 0.20

B. 0.15

C. 0.08

Correct D. 0.11

Correct Answer: D

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Question 23 View Details

A \(12\ \text{V}\) battery has an internal resistance \(r\). When it supplies a lamp of resistance \(R\) the current through the circuit is \(2\ \text{A}\) and the terminal voltage across the lamp is measured to be \(10\ \text{V}\). (a) Find the values of \(r\) and \(R\). (b) Calculate the efficiency of the battery as a percentage.

A. r = 1 Ω, R = 5 Ω, efficiency = 75 %

B. r = 2 Ω, R = 5 Ω, efficiency = 83.3 %

Correct C. r = 1 Ω, R = 5 Ω, efficiency = 83.3 %

D. r = 1 Ω, R = 4 Ω, efficiency = 83.3 %

Correct Answer: C

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Question 24 View Details

A load of \(200\ \text{N}\) is lifted by a rope that passes over a fixed pulley and then under a movable pulley attached to the load. The rope is pulled vertically upward. The movable pulley operates with an efficiency of \(90\%\). Determine the magnitude of the pulling force required to lift the load at constant speed.

A. 90 N

B. 120 N

C. 100 N

Correct D. 111 N

Correct Answer: D

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Question 25 View Details

A rectangular conducting loop of width \(0.10\ \text{m}\) and length \(0.20\ \text{m}\) lies in a uniform magnetic field of magnitude \(0.5\ \text{T}\). Initially the plane of the loop is parallel to the field. The loop is rotated about its longer side (\(0.20\ \text{m}\)) at a constant angular speed of \(60\ \text{rev s}^{-1}\). (a) Find the maximum induced emf in the loop. (b) If the resistance of the loop is \(0.05\ \Omega\), determine the peak current.

A. emf_max ≈ 3.77 V, peak current ≈ 37.7 A

Correct B. emf_max ≈ 3.77 V, peak current ≈ 75.4 A

C. emf_max ≈ 5.94 V, peak current ≈ 118.8 A

D. emf_max ≈ 2.38 V, peak current ≈ 47.6 A

Correct Answer: B

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