Problems and Solutions on Youngs Modulus of a wire

Problem one and solution

A wire of certain length is having a load at the bottom and correspondingly there is a certain extension. If the same load is immersed in a liquid of certain density,how the elongation is effected ?

While solving this problem we have to understand one point that the force acting on the wire is due to the weight of the body. That means there is an impact of acceleration due to gravity on the weight. When the body is immersed in a liquid there is a force acting in a upward direction called as up thrust which has to be taken into consideration in the second case of the problem. Thus the effective acceleration in this case is going to be less than that of acceleration due to gravity and the problem is solved correspondingly as shown below.

Problem two and solution

A metal wire of certain length under a certain load expands by a value . If the wire is re-casted in such a way that its length is doubled what will be the effect on the extension?

While solving this problem we have to understand one important point that when the length of the wire is doubled its thickness will automatically reduce. Being the volume of the body is always constant,if the length is increased to double, the area is going to be reduced to be half of its original value.

Problem three and solution

Find the effective modulus of elasticity of two different materials when they are connected in series and parallel?

Here we shall understand a small concept in solving this problem .When the wires are connected in series, being the load is applied at the bottom of the combination the similar force acts on both of them but each were expands differently because of the nature that they have.

When the two words are connected in parallel as the applied force is the same common force on both of them it is going to be shared across these two wires. Thus they are going to have same extension.