Hooke's law and elasticity — AS & A Level Further Mathematics (9231) questions by topic
Hooke's law problems here combine springs, elastic strings and circular motion: finding the extension of a vertical spring supporting a particle, analysing a particle on a rotating disc attached by an elastic string, and finding the extension of a string on an inclined plane.
Find and show are the two top command words across 21 questions from 2023 to 2025 papers, worth from 3 to 9 marks, so setting up the correct tension-extension relationship early is usually the deciding step. With no examiner-report extracts logged for this topic, submitting each equilibrium or energy equation for instant marking is the main way to confirm the modulus of elasticity has been applied correctly before the rest of the solution builds on it.
May–June 2025, Paper 31
A rough horizontal disc, centre O, rotates with constant angular speed omega rad s^-1. A particle P of mass 1.6 kg lies on the disc at a distance 1.5 m from O, and is attached to…
Answer this question and get it marked →May–June 2025, Paper 32
A rough horizontal disc, centre O, rotates with constant angular speed omega rad s^-1. A particle P of mass 1.6 kg lies on the disc at a distance 1.5 m from O, and is attached to…
Answer this question and get it marked →One end of a light elastic string of natural length 0.5 m and modulus of elasticity 14 N is attached to a fixed point A on a smooth plane. The plane makes an angle alpha to the…
Answer this question and get it marked →May–June 2025, Paper 33
A particle P of mass m is attached to one end of a light elastic string of natural length a and modulus of elasticity mg. The other end of the string is attached to a fixed point…
Answer this question and get it marked →May–June 2025, Paper 34
A light spring of natural length a and modulus of elasticity 20mg is placed so that it stands vertically on a horizontal plane. The lower end of the spring is fixed to the plane.…
Answer this question and get it marked →May–June 2024, Paper 31
The points A and B are at the same horizontal level a distance 4a apart. The ends of a light elastic string, of natural length 4a and modulus of elasticity lambda, are attached to…
Answer this question and get it marked →May–June 2024, Paper 32
The points A and B are at the same horizontal level a distance 4a apart. The ends of a light elastic string, of natural length 4a and modulus of elasticity lambda, are attached to…
Answer this question and get it marked →May–June 2024, Paper 33
A particle P of mass m is attached to one end of a light elastic string of natural length a and modulus of elasticity 2mg. A particle Q of mass km is attached to the other end of…
Answer this question and get it marked →October–November 2024, Paper 31
A particle P of mass m kg is attached to one end of a light elastic string of natural length 2 m and modulus of elasticity 2mg N. The other end of the string is attached to a…
Answer this question and get it marked →October–November 2024, Paper 32
A particle of mass 2 kg is attached to one end of a light elastic string of natural length 0.8 m and modulus of elasticity 100 N. The other end of the string is attached to a…
Answer this question and get it marked →A particle P of mass m is attached to one end of a light elastic spring of natural length a and modulus of elasticity 5mg. The other end of the spring is attached to a fixed point…
Answer this question and get it marked →October–November 2024, Paper 33
A particle P of mass m kg is attached to one end of a light elastic string of natural length 2 m and modulus of elasticity 2mg N. The other end of the string is attached to a…
Answer this question and get it marked →May–June 2023, Paper 31
One end of a light elastic string, of natural length a and modulus of elasticity 3mg, is attached to a fixed point O. The other end of the string is attached to a particle P of…
Answer this question and get it marked →A light elastic string of natural length a and modulus of elasticity lambdamg has one end attached to a fixed point O on a smooth horizontal surface. When a particle of mass m is…
Answer this question and get it marked →May–June 2023, Paper 32
One end of a light elastic string, of natural length a and modulus of elasticity 3mg, is attached to a fixed point O. The other end of the string is attached to a particle P of…
Answer this question and get it marked →A light elastic string of natural length a and modulus of elasticity lambdamg has one end attached to a fixed point O on a smooth horizontal surface. When a particle of mass m is…
Answer this question and get it marked →May–June 2023, Paper 33
One end of a light elastic string, of natural length a and modulus of elasticity lambda m g, is attached to a fixed point O. The string lies on a smooth horizontal surface. A…
Answer this question and get it marked →One end of a light elastic string, of natural length 12a and modulus of elasticity k m g, is attached to a fixed point O. The other end of the string is attached to a particle of…
Answer this question and get it marked →October–November 2023, Paper 31
A light elastic string has natural length 8a and modulus of elasticity 5mg. A particle P of mass m is attached to the midpoint of the string. The ends of the string are attached…
Answer this question and get it marked →October–November 2023, Paper 32
A particle P of mass m is attached to one end of a light rod of length 3a. The other end of the rod is able to pivot smoothly about the fixed point A. The particle is also…
Answer this question and get it marked →October–November 2023, Paper 33
A light elastic string has natural length 8a and modulus of elasticity 5mg. A particle P of mass m is attached to the midpoint of the string. The ends of the string are attached…
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