GCSE & IGCSE physics practice

Hooke's law questions and answers

Hooke's law says the extension of a spring is proportional to the force on it, up to the limit of proportionality: $F = ke$ , where $k$ is the spring constant in N/m and $e$ is the extension in m. The energy stored in a stretched spring is $E_e = \tfrac{1}{2}ke^2$ .

15 questions · Foundation tier · Every answer is checked as you type it, with a full worked solution. Updated 10 Nov 2026.

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Where hooke's law comes up

GCSE (AQA)	Physics and Combined Science, Foundation and Higher. Recall F = ke (on AQA's list of equations to learn); Ee = ½ke² is given on the equation sheet. Investigating force and extension is a required practical.
Cambridge IGCSE (0625)	Supplement (Extended): define the spring constant as force per unit extension and recall and use k = F ÷ x; use the limit of proportionality. Core: interpret load–extension graphs.

The method

Extension = stretched length − original length.
F = k × e: force in N, extension in m.
Rearranged: k = F ÷ e and e = F ÷ k.
Energy stored: Ee = ½ × k × e².

Hooke's law questions

Try each one before looking at the hint. If you're stuck, the AI tutor can talk you through it step by step.

Warm-up

Question 1Warm-upFoundation

A spring has a spring constant of 40 N/m. What force stretches it by 0.05 m?

Question 2Warm-upFoundation

A force of 6 N stretches a spring by 0.12 m. Calculate the spring constant.

N/m

Question 9Warm-upFoundation

A spring has a spring constant of 30 N/m. What force stretches it by 0.2 m?

Question 10Warm-upFoundation

A force of 12 N stretches a spring by 0.04 m. Calculate the spring constant.

N/m

Exam-style

Question 3Exam-styleFoundation

A spring with $k = 200$ N/m has a 10 N force applied. Calculate its extension.

Question 4Exam-styleFoundation

A spring is 20 cm long. With a 3 N weight hung on it, it is 26 cm long. Calculate the spring constant in N/m.

N/m

Question 5Exam-styleFoundation

A spring has $k = 25$ N/m. What force gives an extension of 8 cm?

Question 6Exam-styleFoundation

A spring with $k = 80$ N/m is stretched by 0.1 m. How much elastic potential energy does it store?

Question 11Exam-styleFoundation

A spring with $k = 500$ N/m has a 25 N force applied. Calculate its extension in cm.

Question 12Exam-styleFoundation

A spring is 15 cm long. With a 4 N weight hung on it, it is 23 cm long. Calculate the spring constant in N/m.

N/m

Question 13Exam-styleFoundation

A spring with $k = 200$ N/m is stretched by 0.15 m. How much elastic potential energy does it store?

Challenge

Question 7ChallengeFoundation

A 2 kg mass hangs on a spring with $k = 196$ N/m. Calculate the extension. ( $g = 9.8$ N/kg)

Question 8ChallengeFoundation

A spring obeys Hooke's law up to 4 N. When 6 N is hung on it, the extension is more than 1.5 times the 4 N extension. Why?

Question 14ChallengeFoundation

A 0.5 kg mass hangs on a spring with $k = 49$ N/m. Calculate the extension. ( $g = 9.8$ N/kg)

Question 15ChallengeFoundation

A spring stores 0.9 J of elastic potential energy when stretched by 0.06 m. Calculate its spring constant.

N/m

Common mistakes

Using the stretched length instead of the extension.
Leaving the extension in cm.
Forgetting to square the extension in ½ke².

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Sources

The questions are our own. The “where it comes up” notes are from each board's published specification, checked on 27 October 2026:

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