# NCERT Class 11 Physics Solutions: Chapter 9 – Mechanical Properties of Solid-Part 1 (For CBSE, ICSE, IAS, NET, NRA 2023)

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**Question 9.1**:

A steel wire of length and cross-sectional area stretches by the same amount as a copper wire of length and cross-sectional area of 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,

Area of cross-section of the steel wire,

Length of the copper wire,

Area of cross-section of the copper wire,

Change in length

Force applied in both the cases

Young՚s modulus of the steel wire:

Young՚s modulus of the copper wire:

Dividing we get:

The ratio of Young՚s modulus of steel to that of copper is

**Question 9.2**:

Figure shows the strain-stress curve for a given material. What are

Young՚s modulus and

Approximate yield strength for this material?

**Answer**:

Young՚s modulus:

It is clear from the given graph that for stress , strain is

Young՚s modulus

Hence, Young՚s modulus for the given material is .

Approximate yield strength for this material:

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

**Question 9.3**:

The stress-strain graphs for materials and are shown in Figure.

The graphs are drawn to the same scale.

(a) Which of the materials has the greater Young՚s modulus?

(b) Which of the two is the stronger material?

**Answer**:

(a) The materials has the greater Young՚s modulus:

**Explanation**:

For a given strain, the stress for material is more than it is for material , as shown in the two graphs.

Young՚s modulus

For a given strain, if the stress for a material is more, then Young՚s modulus is also greater for that material. Therefore, Young՚s modulus for material is greater than it is for material .

(b) The two is the stronger material:

**Explanation**:

The amount of stress required for fracturing a material, corresponding to its fracture point, gives the strength of that material. Fracture point is the extreme point in a stress# strain curve. It can be observed that material can withstand more strain than material . . Hence, material . is stronger than material .