Physics · Properties of bulk matter · chapter 8 of 14

Class 11 Physics Chapter 8: Mechanical Properties of Solids case study question with answers

One case-based question of the kind CBSE-pattern school exams ask: a passage and a table, then 3 parts worth 4 marks in all, with the answer and the marking scheme for each. Written from the NCERT chapter.

Case study · 4 marks

In a school laboratory in Pune, Kavya hangs a wire 2.0 m long and 0.50 mm in diameter from a rigid support and adds slotted weights to a hanger at its lower end. With a vernier she measures the extension after each addition, keeping well within the elastic limit. Her readings are in the table. She plans to identify the metal by comparing her value of Young's modulus with Table 8.1.

Load (N)	0	10	20	30	40
Extension (mm)	0	0.51	1.02	1.53	2.04

Part 1 · 1 mark

The extension she should expect with a load of 25 N is about

(a) 1.02 mm(b) 1.28 mm(c) 1.53 mm(d) 2.55 mm

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Answer: (b) 1.28 mm

Extension is proportional to load: 0.51 mm per 10 N, so 25 N gives 2.5 × 0.51 = 1.28 mm.

Part 2 · 2 marks

Calculate the Young's modulus of the wire from her readings.

Answer and marking scheme

A = πr² = 3.14 × (0.25 × 10⁻³)² = 1.96 × 10⁻⁷ m². From the table, 10 N gives ΔL = 0.51 × 10⁻³ m. Y = FL/(AΔL) = (10 × 2.0)/(1.96 × 10⁻⁷ × 0.51 × 10⁻³) = 2.0 × 10¹¹ N m⁻².

area 1.96 × 10⁻⁷ m² (1)
Y = FL/(AΔL) = 2.0 × 10¹¹ N m⁻² (1)

Calculate the stress and the strain in the wire when the load is 40 N.

Answer and marking scheme

A = π(0.25 × 10⁻³)² = 1.96 × 10⁻⁷ m². Stress = 40/1.96 × 10⁻⁷ = 2.04 × 10⁸ N m⁻². Strain = 2.04 × 10⁻³ m/2.0 m = 1.02 × 10⁻³.

stress = 2.04 × 10⁸ N m⁻² (1)
strain = 1.02 × 10⁻³ (1)

Part 3 · 1 mark

Comparing with Table 8.1, the wire is most likely made of

(a) aluminium(b) copper(c) steel(d) glass

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Answer: (c) steel

Y ≈ 2.0 × 10¹¹ N m⁻² = 200 GPa, the value for steel. Copper is 110 GPa and aluminium 70 GPa.

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