Mechanical Properties Of Solids

Given that the strain produced is 0.2% (or 0.002) and the Young's modulus is , calculate the area of the cross-section that can support a load of .

Step 1: Young's Modulus and Stress Relationship

Young's modulus ( ) is defined as the ratio of stress to strain:

Rearranging this equation to find stress:

Step 2: Substituting the Given Values

The given strain is (which is 0.2%), and the Young's modulus is .

Substitute these values into the stress equation:

Step 3: Solving for the Area

The stress is the force per unit area. We can rearrange the equation to solve for the area:

Substitute the given force of and the calculated stress :

So, the area is:

Therefore, the area of the cross-section that can support a load of 104 N is approximately: , which corresponds to option (A) 7.1 x 10^-4 m².

The center of mass and the center of gravity are related concepts but have key differences:

Center of Mass:

• The center of mass of an extended body is the point where the entire mass of the body can be considered to be concentrated.
• It is the average position of all the individual particles' masses that make up the body.
• The center of mass is determined based on the distribution of mass within the object.

Center of Gravity:

• The center of gravity is the point where the force of gravity can be considered to act on the body.
• In a uniform gravitational field, the center of gravity coincides with the center of mass.
• In non-uniform gravitational fields, the center of gravity may differ slightly from the center of mass.

In summary: The center of mass is related to mass distribution, while the center of gravity is related to the distribution of the gravitational force. In most practical situations where gravity is uniform, the two points coincide.

Given:

• Young's modulus: N/m
• Poisson's ratio:
• Lateral strain:

Step 1: Relationship Between Lateral and Longitudinal Strain

Poisson’s ratio is given by:

Rearranging for longitudinal strain :

Step 2: Elastic Energy Density Formula

The elastic energy density is given by:

Substituting values:

Answer: The correct option is D (16 × 10⁵ J/m³).