Hooke's Law - UNSOLVED PRACTICE SET

Q7. State Hooke's law. Write its mathematical form and define each term.

Q8. A wire of length L and cross-sectional area A is stretched by a force F. Show that the extension ΔL is given by ΔL = FL/AY, where Y is Young's modulus.

Q9. A spring extends by 2 cm when a load of 50 g is hung from it. Calculate the force constant of the spring. (Take g = 9.8 m/s²)

Q10. In your school, a student finds that a rubber band stretches much more than a steel wire for the same applied force. Does this mean rubber obeys Hooke's law better than steel? Explain.

Q11. Why does Hooke's law fail beyond the elastic limit? Explain at the molecular level.

Q12. Two springs A and B have force constants k₁ and k₂ respectively. They are stretched by the same force F. Compare their extensions.

Q13. State and explain Hooke's law. Discuss its limitations and the conditions under which it is valid. Explain why elastomers (like rubber) do not obey Hooke's law over a wide range of strain, while metals do within their elastic limit. Draw stress-strain curves for both materials and compare.

Q14. A wire of length 3 m and radius 0.5 mm is stretched by a load of 10 kg. Young's modulus of the material is 7 × 10¹⁰ N/m².

(a) Calculate the stress in the wire.

(b) Calculate the strain in the wire.

(c) Calculate the extension of the wire.

(d) If the elastic limit corresponds to a stress of 2.5 × 10⁸ N/m², has the elastic limit been exceeded?

(e) Calculate the maximum load the wire can bear without exceeding the elastic limit.

Q15. Analyse the following statement: "Hooke's law is not a fundamental law of nature like Newton's laws, but rather an empirical observation." Discuss:

(a) What makes a law "fundamental" versus "empirical"

(b) Why Hooke's law is considered empirical

(c) The molecular basis that explains why Hooke's law works for small deformations

(d) Situations where Hooke's law breaks down

(e) Whether Hooke's law can be derived from more fundamental principles

Q16. In a school experiment, a student investigates the extension of a steel wire:

Original length = 2 m

Diameter = 0.4 mm

Successive loads and corresponding extensions are recorded

(a) Calculate the cross-sectional area of the wire.

(b) If a 2 kg mass produces an extension of 1.6 mm, calculate Young's modulus.

(c) Plot a graph of load vs extension and explain its shape.

(d) At what load would you expect the student to observe deviation from linearity?

(e) If the student uses a copper wire of the same dimensions, how would the graph differ?

Q17. A spring balance in your school laboratory has a scale reading from 0 to 50 N. The length of the scale is 10 cm.

(a) Calculate the force constant of the spring.

(b) What is the extension when a 30 N weight is hung?

(c) If the spring is made of steel wire of diameter 1 mm and original length 20 cm, calculate Young's modulus of steel using this data.

(d) What is the maximum mass that can be measured without exceeding the elastic limit, if the elastic limit strain is 0.002?

(e) Discuss why spring balances are calibrated in newtons rather than kilograms.

Q18. Two springs with force constants k₁ = 100 N/m and k₂ = 200 N/m are available in the physics lab.

(a) Calculate the equivalent force constant when they are connected in series.

(b) Calculate the equivalent force constant when they are connected in parallel.

(c) A 5 kg mass is hung from the series combination. Calculate the total extension.

(d) The same mass is hung from the parallel combination. Calculate the extension of each spring.

(e) Which combination would you use for a sensitive measuring instrument, and why?