The Problem:
Three equal masses, each weighing 3kg, are connected by a massless string. The cross-sectional area of the string is 0.005cm and its Young's modulus is 2×10^11 N/m. In the absence of friction, what is the longitudinal strain in the wire?

Understanding the Problem:
To solve this problem, we need to understand the concepts of mass, weight, cross-sectional area, Young's modulus, and strain. Let's break down each of these concepts:

1. Mass: Mass is the measure of the amount of matter in an object. In this case, each of the three masses is 3kg.

2. Weight: Weight is the force exerted by an object due to gravity. It is calculated by multiplying the mass of the object by the acceleration due to gravity. In this case, the weight of each mass is given by W = m * g, where m is the mass and g is the acceleration due to gravity (approximately 9.8 m/s^2).

3. Cross-sectional Area: The cross-sectional area of an object is the area of the shape formed when it is cut perpendicular to its length. In this case, the cross-sectional area of the string is given as 0.005cm.

4. Young's Modulus: Young's modulus is a measure of the stiffness of a material. It describes the ratio of stress to strain in a material under tension or compression. In this case, the Young's modulus of the string is given as 2×10^11 N/m.

5. Strain: Strain is a measure of the deformation of an object relative to its original length. It is calculated by dividing the change in length of the object by its original length.

Now let's move on to calculating the longitudinal strain in the wire.

Solution:

1. Calculating the Weight:
Since each mass weighs 3kg, the weight of each mass can be calculated as follows:
Weight = mass * acceleration due to gravity
Weight = 3kg * 9.8 m/s^2
Weight = 29.4N

2. Calculating the Total Force:
Since the three masses are connected by a massless string, the total force acting on the string is the sum of the weights of the three masses. Therefore, the total force is given by:
Total Force = 29.4N + 29.4N + 29.4N
Total Force = 88.2N

3. Calculating the Stress:
Stress is defined as the force per unit area. In this case, the stress in the wire is given by:
Stress = Total Force / Cross-sectional Area
Stress = 88.2N / (0.005cm * 10^-4 m/cm)
Stress = 88.2N / (5 * 10^-6 m^2)
Stress = 1.764 * 10^7 N/m^2

4. Calculating the Longitudinal Strain:
Using Young's modulus, the longitudinal strain can be calculated as follows:
Strain = Stress / Young's Modulus
Strain = (1.764 * 10^7 N/m^2) / (2 * 10^11 N/m)
Strain = 8.82 * 10^-5

Therefore, the longitudinal