IIT JEE and NEET Physics @ Venkats Academy IIT-JEE and NEET Physics

Surface tension is the property of a liquid because of which the surface behaves like a stretch the elastic membrane. Surface tension is due to the inter molecular force of attraction between the molecules of the liquid. The molecular force is always an attractive force. The molecular force of attraction between the similar kind of molecules is called a cohercive force and the molecular force of attraction between the different kinds of molecules is called as an adhesive force. Both of them are always an attractive forces.

Each molecule can influence the surrounding molecules up to certain distance and this particular distance is called as a molecular range. Taking the molecule as the centre and the molecular range is a radius if a sphere is drawn,then that is called a sphere of influence. Within the sphere of influence, the given molecule can influence the surrounding molecules.

Surface tension is defined as a tangential force acting per unit length at right angles to the either side of the imagined line drawn on the free liquid Surface of the liquid in the equilibrium state.

To understand the direction of the surface tension force,we shall imagine a line on the surface of the liquid. At right angles to the either side of the line if you draw a tangential line, it gives the direction of the force and the direction of the surface tension. This is treated as a scalar physical quantity.

A small needle is able to float on the surface of the liquid because of the surface tension force.

A small insect is able to walk on the surface of the water due to the surface tension. Here the weight of the small insect is able to be compensated by the force due to the surface tension in the opposite direction , therefore it is not sinking down.

When we are using the length in the definition of the surface tension we shall write the free length of the surface. Under different circumstances the length of the free surface will change and correspondingly the force due to the surface tension also change as shown below. When you are dealing with the wire it will how two free surfaces where as when we are dealing with a closed body like a metal body it will have only one free surface.

Problem and solution

When a wire of length l and a cross-sectional radius r is floating on the surface of the liquid, find the minimum surface of the wire such that it may not sink ?

While we are solving this problem, we shall consider that the weight is acting in the downward direction and is compensated by the force due to the surface tension. Therefore at the equilibrium state we can just equate this two forces.

Problem and solution

A liquid is contained in a vertical Tube of a semicircular cross-section find the ratio of the force of surface tension on the circular part as well as the flat part?

In solving this problem we have to count the surface length of the liquid bit carefully. The 1^st case it is half of the circumference of the circle it is in the second case it the flat part and is nothing but the diameter of the circle.

Problems and Solutions on Young's Modulus of a wire

Rigidity Modulus and Bulk Modulus

Behavior of a Wire under Increasing Load

Breaking Stress and Its Applications

Experimental determination of Youngs modulus of the wire

Energy stored in the wire

Problems and Solutions on Elasticity

Problem and solution

A metal ring of radius r and cross-section is a has to be fixed than a wooden circular disc of radius R. Assume that the radius of the disc is greater than that of the ring. What is the force acting on the ring ?

To fix the ring of the disc, we shall increase the size of the ring that is at least equal to the size of the disk. That is why we shall apply a force on the ring therefore its radius can be increased.

Problem and solution

A light rod of length 2 meter is suspended from the ceiling horizontally by means of the 2 vertical wires of the same length as shown.

One of the wire is made up of the steel and other one is made up of the brass and their respective areas of cross-sections are given. Find the position along the broad at which a weight has to be suspended so that there may be equal stress on the both the wires and also find the location of the weight so that there will be equal strains on both the wires?

Density of the compressed liquid

Compressibility can be defined as the reciprocal of the bulk modulus. We can derive the equation for the density that how it is being effected if an external force is applied as shown below. We know as per the concept of the bulk modulus in the place of the change of the volume even we can write the change in the density and derive the equation as shown below.

Poisons ratio can be defined as the ratio of lateral strain to that of the longitudinal strain. Lateral strain is defined as the ratio of decreasing the thickness of the wire with respect to its original thickness. Longitudinal strain is defined as the ratio of increase the length of the wire to its original length.

These two strains are perpendicular to each other. While the longitudinal strain increases the length of the wire, the lateral strain decreases the thickness of the wire and hence it is shown with a negative sign.

Problem and solution

In the 1^st problem volume of the material is given for you and it is also given that it is subjected to how much of the pressure if the corresponding change in the volume is also given in the problem we have to calculate the bulk modulus?

There are two more different problems in the given now diagram and it can analyse them and comment back if you are having any doubts.

We have two more pages of the problems and solutions as attached below. You can go through the diagram by zooming in and you can comment at the end of the page ,if you are having any of the doubts regarding them.

While solving the first problem law of conservation of energy is taken into consideration.When the wire is stretched it has some energy called strain energy and this is converted into kinetic energy.

In solving the second problem we have taken into count that the increase in the length is directly proportional to the applied force on the wire when all other terms are constant.

In solving the first problem we shall understand that the volume of the wire is constant.When its area changes,its length will change but total volume remains constant.

While solving the last problem, we are dealing with the weight of the body suspended.We can express that mass in terms of volume and density of the body and hence extension is directly proportional to its cube of the radius of the suspended body in spherical shape.