## Monday, December 19, 2016

### Mechanical Properties of Solids Problems with Solutions One

We are going to solve series of problems on the physics topics mechanical properties of solids.We basically deal about the property called elasticity. It is the property of the body due to which it is able to regain its original position after removing the external force that is applied on that body. It is because of inter molecular force of attraction and restoring force of the molecules of the body. If the body is able to recover back to its original position well, then it is called elastic body and if not it is called a plastic body. We need to know that no body is perfectly elastic and no body is perfectly elastic.

Problem

When a metal sphere is suspended at the end of a metal wire, its extension is 0.4 millimeter. If another sphere of same materiel with the radius half to the first radius is suspended from the same wire, we need to find the extension in the wire. Problem is as shown in the diagram below.

Solution

Extension in the wire is directly proportional to the force applied on the wire. It is nothing but the weight of the sphere that is suspended. As the radius is given in the problem, we need to write its mass as the product of volume and density and volume is directly proportional to the cube of  the radius. So the extension of the wire is directly proportional to the cube of the radius of the load suspended and the problem can be further solved as shown in the diagram below.

Problem

The diameters of two steel wires are in the ratio of 2:3 and their lengths are equal.When same force is applied on both of them, we need to find the ratio of elongation produced in the two wires and the problem is as shown in the diagram below.

Solution

We can write the elongation of the wire in terms of the load applied and it is given in the problem that the load is same. So the stress as well as extension is inversely proportional to the area of cross section or inversely proportional to the square of the radius of the wire. Problem can be solved further as shown in the diagram below.

Problem

Area of cross section of the wire and the ratio  of extension of the wire in terms of its initial length is also given to us in the problem. We know the applied force and we need to find the young's modulus of the wire and the problem is as shown in the diagram below.

Solution

We know that young's modulus of the wire as the ratio of longitudinal stress to the longitudinal strain. Stress is defined as the ratio of applied force to the area of cross  section of the body and the stain is the ratio of change in the length to its original length. Problems data can be applied and solved as shown in the diagram below.

Problem

Two wires are made up of same material and their lengths and diameters ratio is given to us in the problem. If they are stretched by the same force, we need to find the ratio of the extensions in the two wires and the problem is as shown in the diagram below.

Solution

As the wires are same, their young''s modules is same for both of them. We can write equation for the elongation based on the defination  of the Young's modules and the problem can be further solved as shown in the diagram below.

Problem

If a rubber ball is taken into a 100 meter depths of water, its volume is changed by certain percentage and we need to measure the bulk modules of that material and the problem is as shown in the diagram below.

Solution

We know that bulk modulus is defined as the ratio of bulk stress to the bulk strain. Bulk stress is similar to the pressure applied on the system and it can be expressed in terms of the depth of the water. Bulk strain is the ratio of change in the volume of the body when compared with its initial volume. Data can be applied and problem can be solved as shown in the diagram below.

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