Stress and Strain – Types - UNSOLVED PRACTICE SET

Q7. Define stress and strain. Name the three types of stress and the corresponding types of strain.

Q8. Distinguish between tensile stress and compressive stress. Give one example of each.

Q9. What is shearing strain? Explain with a diagram how it is produced.

Q10. In your school, a student stands on a wooden plank supported at both ends. Identify the type of stress produced in:

(a) The plank

(b) The supporting pillars

Q11. A cube of side 10 cm is subjected to a uniform pressure of 10⁵ Pa on all faces. Calculate the volumetric strain if the bulk modulus of the material is 10¹⁰ Pa.

Q12. Why does the cross-sectional area of a wire decrease when it is stretched? What type of strain is this?

Q13. Explain the different types of stress and strain with diagrams:

(i) Longitudinal (tensile and compressive) stress and strain

(ii) Shearing stress and shearing strain

(iii) Hydraulic stress and volumetric strain

For each type, give two real-life examples and explain the physical significance.

Q14. A wire of length 2 m and cross-sectional area 10⁻⁶ m² is stretched by a force of 20 N.

(a) Calculate the longitudinal stress.

(b) If the extension is 2 mm, calculate the longitudinal strain.

(c) A cube of the same material of side 0.1 m is subjected to a shearing force of 1000 N on its top face, causing a displacement of 0.01 mm. Calculate the shearing stress and strain.

(d) The same cube is subjected to a uniform pressure of 10⁷ Pa. Calculate the volumetric strain if the bulk modulus is 1.5 × 10¹⁰ Pa.

(e) Compare the magnitudes of the three types of strain.

Q15. Analyse the deformation produced in the following situations and identify the type of stress and strain involved:

(a) A pillar supporting a building

(b) A nail being hammered into wood

(c) A book pushed sideways on a table

(d) A submarine diving deep into the ocean

(e) A wire being pulled from both ends

For each case, discuss what would happen if the stress exceeds the elastic limit.

Q16. A steel rod of length 2 m and diameter 10 mm is subjected to a tensile force of 5 × 10⁴ N.

(a) Calculate the tensile stress.

(b) If the extension is 2.5 mm, calculate the tensile strain.

(c) Calculate the percentage decrease in diameter if Poisson's ratio is 0.28.

(d) Calculate the new cross-sectional area after stretching.

(e) Verify that the volume change is negligible for small strains.

Q17. A rectangular block of gelatin (10 cm × 10 cm × 5 cm) has its upper face displaced by 0.5 mm when a tangential force of 5 N is applied.

(a) Calculate the shearing stress.

(b) Calculate the shearing strain (in radians).

(c) Calculate the shear modulus of gelatin.

(d) If the same force is applied to a steel block of the same dimensions, how much smaller would the displacement be? (Shear modulus of steel = 84 GPa)

(e) Discuss why gelatin is used in ultrasound gel pads while steel is used in building frames.

Q18. In a school physics lab, students perform an experiment to study different types of strain:

(a) Design an experiment to demonstrate tensile strain using a wire and hanging masses.

(b) Design an experiment to demonstrate shearing strain using a book or rubber block.

(c) Design an experiment to demonstrate volumetric strain using a balloon or sealed container.

(d) For each experiment, list the measurements to be taken and how to calculate the respective strain.

(e) Discuss the safety precautions for each experiment.