INTRODUCTION - Chapter 9 Mechanical Properties Of Solids class 11 ncert solutions Physics - SaraNextGen [2024-2025]

Updated By SaraNextGen

On April 24, 2024, 11:35 AM

Question 9.1:

A steel wire of length 4.7 m and cross-sectional area 3.0 × 10^–5 m² stretches by the same amount as a copper wire of length 3.5 m and cross-sectional area of 4.0 × 10^–5 m² under a given load. What is the ratio of the Young’s modulus of steel to that of copper?

Answer:

Length of the steel wire, L₁ = 4.7 m

Area of cross-section of the steel wire, A₁ = 3.0 × 10^–5 m²

Length of the copper wire, L₂ = 3.5 m

Area of cross-section of the copper wire, A₂ = 4.0 × 10^–5 m²

Change in length = ΔL₁ = ΔL₂ = ΔL

Force applied in both the cases = F

Young’s modulus of the steel wire:

 … (i)

Young’s modulus of the copper wire:

Dividing (i) by (ii), we get:

The ratio of Young’s modulus of steel to that of copper is 1.79 : 1.

Question 9.2:

Figure 9.11 shows the strain-stress curve for a given material. What are (a) Young’s modulus and (b) approximate yield strength for this material?

Answer:

(a) It is clear from the given graph that for stress 150 × 10⁶ N/m², strain is 0.002.

∴Young’s modulus, Y 

Hence, Young’s modulus for the given material is 7.5 ×10¹⁰ N/m².

(b) The yield strength of a material is the maximum stress that the material can sustain without crossing the elastic limit.

It is clear from the given graph that the approximate yield strength of this material is 300 × 10⁶ Nm/² or 3 × 10⁸ N/m².