Deformation of solids — AS & A Level Physics (9702) questions by topic
This page's deformation of solids questions define strain and the Young modulus, derive the Young modulus from a wire's spring constant, and work through stress-strain graphs to elastic potential energy, spanning from 1 to 13 marks.
Calculate, identify and state dominate the command words, alongside deduce and draw: draw a stress-strain line shape correctly rather than guessing its curvature. 60 real questions from 2023 to 2025 papers sit below. Line-by-line submission for instant marking catches an un-squared compression value, an un-converted centimetre-to-metre unit, or premature rounding of stress before cross-sectional area is found, exactly the slips examiners flag most.
What examiners look for
- A common mistake is forgetting to convert compression from centimetres to metres, or not squaring the compression value in the formula.
- Examiners note many forget to convert a spring's mass from grams to kilograms before calculating.
- Reports flag premature rounding: calculating stress and rounding to two significant figures immediately leads to an incorrect cross-sectional area.
- Many candidates appear to guess a stress-strain line shape, most often a straight line from the origin or a curve of decreasing gradient, instead of reasoning it out.
- Only the strongest candidates relate work done on a wire to the area under its graph and to the gain in elastic potential energy.
May–June 2025, Paper 11
A student investigates a spring. The variation of the length of the spring with the force applied to the spring is shown. The graph shows length (m) on the y-axis from 0 to 0.60…
Answer this question and get it marked →The graph shows the variation with force of the extension of a wire. The force is gradually increased to a maximum at Q and then gradually decreased to zero at R. On the…
Answer this question and get it marked →A uniform metal wire of length L and diameter d has spring constant k. What is the Young modulus of the metal? A πd² / (4kL) B πd² / (kL) C kL / (πd²) D 4kL / (πd²)
Answer this question and get it marked →May–June 2025, Paper 12
A student has a copper wire and a steel wire with equal lengths and cross-sectional areas. The student hangs identical loads on the two wires. The extensions of the two wires are…
Answer this question and get it marked →Two springs X and Y stretch elastically. The graphs show the variation with extension x of the force F applied to each spring. Spring X: F rises linearly from 0 to 20 N as x…
Answer this question and get it marked →Which phrase describes the strain at the elastic limit on a stress–strain graph? A the maximum strain below which Hooke's law is obeyed B the maximum strain below which the…
Answer this question and get it marked →May–June 2025, Paper 13
What are the correct units for stress, strain and Young modulus? stress strain Young modulus --- --- --- --- A Pa no unit Pa B Pa Pa no unit C no unit Pa Pa D Pa no unit no unit
Answer this question and get it marked →The graph shows the force–extension relationship for a metal wire that is loaded and then unloaded. The loading curve goes from the origin up to a maximum force (beyond the…
Answer this question and get it marked →A wire has original length L₀ and is stretched to a new length L₁. What is the strain of the wire? A (L₁/L₀) – 1 B (L₁ – L₀) / L₁ C L₁ / L₀ D L₀ / L₁
Answer this question and get it marked →A force–extension graph for a wire of length L is shown, with the limit of proportionality at point P. A second wire made of the same material but with length 2L is loaded in the…
Answer this question and get it marked →May–June 2025, Paper 14
What is the definition of strain? A extension per unit cross-sectional area B extension per unit original length C force per unit cross-sectional area D force per unit extension
Answer this question and get it marked →A spring of unstretched length 0.10 m is suspended vertically from a support. A weight of 2.0 N is attached to the bottom of the spring and its length increases to 0.15 m. An…
Answer this question and get it marked →May–June 2025, Paper 22
May–June 2024, Paper 11
When a force of 0.80 N is applied to a spring, the length of the spring is 90 mm. When a force of 1.30 N is applied to the same spring, its length is 115 mm. The spring obeys…
Answer this question and get it marked →An experiment is carried out using a metal wire to investigate how it responds to a varying tensile force. The cross-sectional area of the wire is constant. Which graph has a…
Answer this question and get it marked →For a wire, Hooke's law is obeyed for a tension F and extension x. The Young modulus for the material of the wire is E. Which expression represents the elastic potential energy…
Answer this question and get it marked →May–June 2024, Paper 12
A sample of metal is subjected to a force which increases to a maximum value and then decreases back to zero. A force–extension graph for the sample is shown, with points X and Y…
Answer this question and get it marked →Two wires, P and Q, made of the same material, are stretched with an increasing force. A graph is plotted of the variation with force of the extension of each wire. Wire P reaches…
Answer this question and get it marked →An extension–force graph for a spring is shown. The graph is a straight line through the origin reaching an extension of 15 cm at a force of 6.0 N. What is the spring constant of…
Answer this question and get it marked →May–June 2024, Paper 13
Two wires, one made of brass and the other of steel, are stretched in an experiment. Both wires obey Hooke's law during this experiment. The Young modulus for brass is less than…
Answer this question and get it marked →A sample of material is stretched by a tensile force to a point beyond its elastic limit. The tensile force is then reduced to zero. The force–extension graph is shown, divided…
Answer this question and get it marked →A wire is fixed at one end and is extended by a force F₁ acting on the other end. This causes the wire to have an elastic potential energy of 0.15 J. The force applied to the wire…
Answer this question and get it marked →May–June 2024, Paper 21
May–June 2024, Paper 22
A pinball machine uses a spring to launch a small metal ball of mass 4.5 x 10^-2 kg up a ramp. The spring is compressed by 8.0 x 10^-2 m and held in equilibrium, as shown in Fig.…
Answer this question and get it marked →May–June 2024, Paper 23
October–November 2024, Paper 11
A spring of spring constant 30 N m^-1 is suspended vertically from its top. The spring obeys Hooke's law. Initially the spring is not compressed and not stretched. A mass of 0.50…
Answer this question and get it marked →A wire has original length L and cross-sectional area A. A tensile force F is applied to the wire which causes it to have extension x. The wire obeys Hooke's law. What is an…
Answer this question and get it marked →A wire is stretched by a gradually increasing force. The force-extension graph for the wire is shown. [Force-extension graph: an initially straight section through point P,…
Answer this question and get it marked →A spring has an unstretched length of 0.30 m and a spring constant of 400 N m^-1. An object is suspended from the spring and the spring is deformed within its limit of…
Answer this question and get it marked →A wire consists of a 3.0 m length of metal X joined to a 1.0 m length of metal Y. The cross-sectional area of the wire is uniform. A load hung from the wire causes metal X to…
Answer this question and get it marked →October–November 2024, Paper 12
Two train carriages each of mass 5000 kg roll toward one another on a horizontal frictionless track. One is travelling at a speed of 2.00 m s^-1 and the other at a speed of 1.00 m…
Answer this question and get it marked →What is a unit for stress? A kg m^-1 s^-2 B kg m^-2 s^-2 C N m^-1 D N m
Answer this question and get it marked →The graph shows the relationship between stress and strain for three wires of the same linear dimensions but made from different materials. P is the steepest straight line, Q is a…
Answer this question and get it marked →Four solid steel rods equally support an object weighing 10 kN. Each rod is of length 2.0 m and cross-sectional area 250 mm^2. The weight of the object causes the rods to contract…
Answer this question and get it marked →October–November 2024, Paper 13
The force-extension graph of a metal wire is shown. The graph is initially a straight line through the origin, with point A at the end of the straight section, then points B and C…
Answer this question and get it marked →A uniform wire is made of a metal that has a Young modulus of 1.3 x 10^11 Pa. The wire is 2.4 m long and has a spring constant of 2.7 x 10^4 N m^-1. What is the volume of the…
Answer this question and get it marked →A rubber cord hangs from a rigid support. A weight attached to its lower end is gradually increased from zero, and then gradually reduced to zero. The force-extension curve for…
Answer this question and get it marked →October–November 2024, Paper 21
Define the Young modulus of a material.
Answer this question and get it marked →October–November 2024, Paper 22
The variation of stress with strain for a metal P is shown in Fig. 3.1. Point E is the elastic limit of the metal. The graph shows stress (in units of 10^7 Pa) on the vertical…
Answer this question and get it marked →October–November 2024, Paper 23
February–March 2023, Paper 12
A spring has an unstretched length of 4.50 cm. The spring is fixed at one end and a force of 35.0 N is applied to the other end so that the spring extends. The spring obeys…
Answer this question and get it marked →A wire is fixed at one end and extended by a force that is applied to the other end. The force is slowly increased from zero and then slowly decreased back to zero. The…
Answer this question and get it marked →February–March 2023, Paper 22
A motor uses a wire to raise a block, as illustrated in Fig. 2.1. The base of the block takes a time of 0.49 s to move vertically upwards from level X to level Y at a constant…
Answer this question and get it marked →May–June 2023, Paper 11
A lamp is suspended in equilibrium from a fixed support by three long identical wires. The weight of the lamp causes each wire to have an extension of 0.40 cm. The height h of the…
Answer this question and get it marked →The force-extension graph for a spring is shown (a straight line through the origin). What represents the work done to extend the spring? A the area under the graph B the gradient…
Answer this question and get it marked →May–June 2023, Paper 12
Two balls, X and Y, approach each other along the same straight line and collide. The collision is perfectly elastic. Their initial speeds are uX and uY respectively. After the…
Answer this question and get it marked →What is meant by the spring constant of a spring? A extension per unit force B (1/2) x force x extension C force x extension D force per unit extension
Answer this question and get it marked →A child holds a thin metal wire that is attached to a kite. The graph shows how the extension of the wire varies with its tension (a straight line through the origin). A gust of…
Answer this question and get it marked →May–June 2023, Paper 13
A perfectly elastic collision occurs between two objects X and Y. The mass of X is m and the mass of Y is 4m. Object X travels at speed v before the collision and speed 3v/5 in…
Answer this question and get it marked →A metal wire has length 5.2 m and diameter 1.0 mm. The metal has Young modulus 360 GPa. The wire is fixed at one end and a force is applied to the other end. The force extends the…
Answer this question and get it marked →The graph shows how the length of a spring varies with the force applied to it (a straight line starting from unstretched length L0 at zero force, rising to length L1 at force F).…
Answer this question and get it marked →May–June 2023, Paper 22
A spring is suspended from a fixed point at one end. The spring is extended by a vertical force applied to the other end. The variation of the applied force F with the length L of…
Answer this question and get it marked →May–June 2023, Paper 23
October–November 2023, Paper 11
An elastic cord of unstretched total length 16.0 cm and cross-sectional area 2.0 x 10^-6 m^2 is held horizontally by two smooth pins a distance 8.0 cm apart. The cord obeys…
Answer this question and get it marked →Which force-extension graph shows plastic deformation of a sample of material? The options A to D show force-extension graphs with loading and unloading curves; the correct graph…
Answer this question and get it marked →October–November 2023, Paper 12
The force-extension graph for a wire is shown, with the extension axis divided into region X (small extension, linear) and region Y (larger extension, curved), and point Z marking…
Answer this question and get it marked →October–November 2023, Paper 13
A copper wire of diameter 1.6 mm is stretched within its limit of proportionality by a tensile force of 430 N. The Young modulus of copper is 130 GPa. What is the strain in the…
Answer this question and get it marked →Compressive forces are applied normally to the end faces of a cylinder of initial length L. The cylinder is compressed by the forces so that its length decreases to 0.6L. After…
Answer this question and get it marked →October–November 2023, Paper 22
A vertical rod is fixed to the horizontal surface of a table, as shown in Fig. 3.1 (not to scale). A spring of mass 7.5 g is able to slide along the full length of the rod. The…
Answer this question and get it marked →October–November 2023, Paper 23
Fig. 4.1 shows the variation with extension x of the tensile force F for two wires, G and H, made from the same material. Both lines are straight through the origin; line H has a…
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