igcse model questions vol1 2023 physics | Essay

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Question 1 View Details
A simple pendulum is set up as shown in the illustration. The length of the string is measured from the point of suspension to the centre of the bob. The string length is recorded as 0.500 m (to the nearest millimetre). Ten complete oscillations are timed with a digital stopwatch and the total time recorded is 14.2 s.
Question Parts
(a)
Explain the correct procedure for measuring the length of the pendulum so that the measurement corresponds to the length required in the period formula.
(b)
Using the data given, calculate the acceleration due to gravity g. Show all steps and state the final answer to two significant figures.
(c)
Identify two possible sources of error in this experiment and explain how each would affect the calculated value of g.
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Question 2 View Details
The motion diagram below shows the positions of two cyclists, X and Y, on a straight road. Positions are recorded at 1‑second intervals. Cyclist X starts from the origin (0 m). Cyclist Y starts 10 m ahead of X. The diagram records the following positions (in metres) at each second:
Question Parts
(a)
Determine the initial speed of cyclist X and the magnitude of its constant acceleration.
(b)
Determine the constant speed of cyclist Y.
(c)
At what time after the start does cyclist X overtake cyclist Y? Show all working.
(d)
Calculate the distance each cyclist has travelled at the moment of overtaking and comment on which cyclist has covered the greater distance and why.
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Question 3 View Details
A student lifts a crate vertically from the floor to a height of 2.5 m. The force required varies with the height because the crate is attached to a spring that stretches as it is lifted. The force‑extension graph is shown below.
Question Parts
(a)
Explain how the area under the force‑extension graph relates to the work done in lifting the crate.
(b)
If the force varies linearly from 0 N at the floor to 150 N at the top, calculate the total work done on the crate. Give your answer in joules (J).
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Question 4 View Details
A metal rod of mass 0.8 kg and specific heat capacity 460 J kg⁻¹ K⁻¹ is heated from 20 °C to 80 °C. The rod is then placed in 200 g of water at 20 °C in an insulated container.
Question Parts
(a)
Calculate the amount of heat energy absorbed by the metal rod during heating.
(b)
Assuming no heat loss to the surroundings, determine the final equilibrium temperature of the water‑metal system. (Specific heat capacity of water = 4 200 J kg⁻¹ K⁻¹.)
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Question 5 View Details
A 2.0 kg block is released from rest at the top of an incline that makes an angle of 30° with the horizontal. The length of the incline is 5.0 m. The coefficient of kinetic friction between the block and the surface is 0.20.
Question Parts
(a)
Calculate the acceleration of the block down the incline.
(b)
Using the acceleration found in part (a), determine the speed of the block after it has travelled the whole 5.0 m down the incline.
(c)
Calculate the total work done by the frictional force during the 5.0 m motion.
(d)
When the block has descended 3.0 m, find the instantaneous power supplied by gravity at that instant.
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Question 6 View Details
The diagram shows a compound pulley system used to lift a load. The system consists of a fixed pulley (P1) attached to the ceiling, a movable pulley (P2) attached to a load L of mass 20 kg, and a single rope that passes over the fixed pulley, under the movable pulley and is then pulled by a hand. The hand pulls the rope through a distance of 2.0 m while the load rises a distance of 0.5 m. When the hand is pulling, a force of 60 N is measured.
Question Parts
(a)
Determine the theoretical (ideal) mechanical advantage of the system using the distances shown in the diagram.
(b)
Calculate the ideal force that must be applied to the rope to lift the 20 kg load, ignoring any friction or other losses.
(c)
The hand actually exerts a force of 60 N. Calculate the efficiency of the system expressed as a percentage.
(d)
Briefly discuss two possible reasons why the efficiency is less than 100 %.
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Question 7 View Details
A sealed cylindrical container of internal cross‑sectional area 0.020 m² contains air at a temperature of 300 K and a pressure of 1.00 × 10⁵ Pa. The container is placed vertically in a deep well filled with water of density 1000 kg m⁻³. The top of the container is level with the water surface. The container is connected to a piston that can move without friction and the piston area is the same as the container cross‑section.
Question Parts
(a)
Calculate the absolute pressure of the air inside the container when the piston is pushed down until it is 5.0 m below the water surface. State any assumptions you make.
(b)
Using the result from part (a), determine the force exerted by the water on the piston at that depth.
(c)
If the piston is now released and allowed to rise back to the water surface, explain qualitatively how the temperature of the trapped air will change and why.
(d)
Briefly describe how the principle demonstrated in this set‑up is applied in a hydraulic lift to raise a heavy load.
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Question 8 View Details
A calorimeter consists of a thin aluminium container (mass 150 g) that holds 200 g of water at 20 °C. An ice cube of mass 50 g at 0 °C is placed in the water and the lid is closed. The specific heat capacities are: cₐₗ = 900 J kg⁻¹ K⁻¹, c_w = 4180 J kg⁻¹ K⁻¹, and the latent heat of fusion of ice L_f = 3.34 × 10⁵ J kg⁻¹. Assume no heat loss to the surroundings.
Question Parts
(a)
Calculate the final equilibrium temperature of the system after the ice has completely melted.
(b)
Determine the total amount of heat energy transferred from the water and aluminium to the ice during the process.
(c)
A metal spoon (thermal conductivity 200 W m⁻¹ K⁻¹) and a wooden spoon (thermal conductivity 0.15 W m⁻¹ K⁻¹) are both placed in the same boiling water (100 °C). Explain why the metal spoon becomes noticeably hotter than the wooden spoon after 30 s, referring to the relevant physical principles.
(d)
If the aluminium container were replaced by a copper container of the same mass (c_cu = 385 J kg⁻¹ K⁻¹, thermal conductivity 400 W m⁻¹ K⁻¹), discuss qualitatively how the final equilibrium temperature and the rate at which equilibrium is reached would be affected.
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Question 9 View Details
A sealed cylindrical steel container has an internal length of 0.500 m and an internal diameter of 0.100 m. It contains 0.16 mol of an ideal gas at a temperature of 300 K and a pressure of 1.0×10^5 Pa. The container is heated uniformly until the gas temperature reaches 400 K. Steel expands linearly with a coefficient of linear expansion of 12×10^-6 K^-1.
Question Parts
(a)
Assuming the dimensions of the container do not change, calculate the new pressure of the gas after heating.
(b)
Now take the thermal expansion of the steel into account and calculate the new pressure of the gas.
(c)
Explain qualitatively how the final pressure would be affected if the container were made of a material with a much larger coefficient of linear expansion.
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Question 10 View Details
The diagram shows a transverse wave travelling to the right along a stretched string. The incident wave has an amplitude of 0.05 m, a wavelength of 0.40 m and a period of 0.20 s. At the right‑hand fixed end the wave is reflected, travelling leftwards with the same amplitude and wavelength but with a 180° phase reversal. The point where the incident and reflected waves cancel (a node) is marked at 0.20 m from the left end of the string.
Question Parts
(a)
Calculate the speed of the incident wave.
(b)
Determine the frequency of the wave.
(c)
Explain why a node occurs at the point 0.20 m from the left end.
(d)
The string is 1.20 m long and both ends are fixed. (i) How many complete standing‑wave loops can be formed on the string? (ii) What is the frequency of the fundamental (first harmonic) standing wave on this string?
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