Mechanical Properties Of Solids

From the formula for Young’s modulus, we have: Where:
is the Young’s modulus,
is the force,
is the cross-sectional area of the wire,
is the change in length,
is the original length of the wire.
We are given that .
The stress is , so: From the equation for Young’s modulus, we can rearrange to find : Substituting :
Thus, the change in length is .

The correct option is (A) : 0

The resistivity of insulators is not independent of temperature. In fact, for insulators, the resistivity decreases with increasing temperature, though it is much more sensitive than in conductors. The resistivity of conductors increases with temperature, whereas in semiconductors and insulators, it decreases as more charge carriers are available at higher temperatures. Thus, the incorrect statement is, as resistivity of insulators is not independent of temperature.

The correct option is (E) : Resistivity of insulators is independent of temperature

Step 1: Initial Work to Form Bubble

Work required to form bubble of radius R:

(where γ is surface tension)

Step 2: Work for Increased Radius

For radius R + ΔR:

Step 3: Expand and Find ΔW

(for small ΔR)

Step 4: Calculate Ratio

Given :

Step 1: Understand the Given Parameters

We are given:

• Applied pressure (P) = 100 atm
• Bulk modulus (B) = 10¹¹ N/m²

Step 2: Convert Pressure to SI Units

1 atm = 1.01325 × 10⁵ N/m²

Step 3: Apply Bulk Modulus Formula

The bulk modulus formula relates pressure change to volume change:

For small changes, the fractional volume change is:

Step 4: Calculate Fractional Volume Change

The negative sign indicates volume decreases under pressure.

Step 5: Convert to Percentage

Given:

• Natural length of wire,
• Cross-sectional area,
• Mass hung, (force )
• Elastic potential energy,
• Acceleration due to gravity,

Step 1: Relate Energy to Extension

Elastic potential energy in a stretched wire is given by:

Solve for extension :

Step 2: Calculate Young's Modulus (Y)

Young's modulus is defined as:

Substitute values:

Conclusion:

The Young's modulus of the wire is .

Answer:

Step 1: Young’s modulus ( ) measures the stiffness of a material and is defined as:
Step 2: The values of Young’s modulus for common metals are:
Aluminium: Pa
Copper: Pa
Brass: Pa
Steel: Pa
Wrought Iron: Pa
Step 3: Since steel has the highest Young’s modulus, it is the stiffest material among the given options.
Step 4: Therefore, the correct answer is (D). \bigskip