Duduli

The polarizability of a hydrogen atom describes how easily it's electron cloud can be distorted by an external electric field.

The rank of the tensor is the number of suffixes or indices(without counting an index which appears once as a subscript) in the symbol representing tensor.

It is a device which is used to produce the plane polarised light. It is based on the principle of selective absorption and more effective than the tourmaline crystal. Polaroid allows the light oscillations parallel to the transmission axis to pass through them. The crystal or polaroid on which the unpolarised light is incident is called polariser. Crystal or polaroid on which polarised light is incident is called analyser.

It is defined as the angle between the tangent to the liquid surface at the point of contact and solid surface inside the liquid is called as angle of contact  The value of angle of contact depends upon  (i) Nature of solid and liquid in contact  (ii) Cleanliness of the surface in contact  (iii) Medium above the free surface of liquid 

The loop formed by loading and unloading the wire is called hysteresis loop.

Carbon nanotube(CNT) is an allotrope of carbon. There are two types of CNT namely single walled carbon nanotube(SWNT) and multi walled carbon nanotube(MWNT). Single walled carbon nanotube is a one thick sheet of graphite(graphene) rolled up into a seamless cylinder with diameter of the order of a nanometer. In SWNT the length to diameter exceeds 1,000000. Multi walled carbon nanotube is made up of a number of concentric tubes.

It is an optical device made from calcite crystal & is used in many optical instruments for producing & analysing plane polarized light. It derives its name from its inventor William Nicol who first designed it 1828. It is based on the phenomenon of double refraction when an unpolarized light ray passes through a calcite crystal it splits into 2 refracted rays i.e o-ray & E-ray. The vibrations of E-ray are in the plane of paper while those of o-ray are perpendicular to plane of paper. Both these rays are plane polarized & are perpendicular to each other. For obtaining only single polarized beam, we should eliminate the other beam. Nicol prism is made in such a way that it eliminates o-ray by TIR & only E-ray comes out of the prism.

A double pendulum consists of two masses connected by an inextensible light rod. The system of two masses and the rod is suspended by another inextensible and weightless rod fastened to one of the masses as shown in the figure In another way a double pendulum may be described as follows: As the name indicates a double pendulum may be supposed to be formed of two pendular oscillating in the same plane; one has a Bob of mass m1 suspended from a flat hinge at O by an inextensible and weightless rod of length l1, while the other has a rod of mass m2 suspended from another hinge in mass m1 by a similar rod of length l2.

A frame attached with the centre of mass of an isolated system of particles is called at the centre of mass coordinate system or C-system.

It is to be noted that the Hamiltonian equations are specially used to solve the problems involving cyclic coordinates. A coordinates qk is cyclic if it does not appear in the lagrangian. Cyclic coordinate is the coordinate for which corresponding momentum remains conserved.

If the work done by a force is independent of path, the force is said to be conservative. If the forces acting on the particles are conservative: it's mechanical energy(kinetic energy+potential energy) remains constant.This is called conservation of energy.

According to Hamilton's principle,“The path actually traversed in a conservative, holonomic dynamical system from t1 & t2 is one over which the integral of the lagrangian between limits t1 & t2 is stationary (i.e the time integral of the lagrangian is extremum.) Analytically it can be represented as    ∫L dt = J = extremum Where J is the extremum value of the time integral of the lagrangian and is known as Hamilton's principle function for the path. Or  d[ ∫L dt ]=0 Where 'd' is the variation symbol. This principle helps us to distinguish the actual path from the neighbouring paths.

The constraints which are dependent on time are known as rheonomic constraints. e.g a simple pendulum suspended with a moving support i.e pendulum having variable length is an example of rheonomic constraint.

The constraints which are independent of time are known as scleronomic constraints. e.g a simple pendulum suspended with fixed support i.e length of the pendulum remains constant is an example of scleronomic constraints.

Constraints are said to be holonomic if constraints imposed on the motion of the system can be expressed in the form of mathematical equation f(r1,r2,.....,rn,t)=0.  where r1,r2,.....,rn are position vector of system of particles & 't' is time. Example of holonomic constraints  ★The constraints involved in the motion of rigid bodies in which the distance between two particular points is always fixed. ★The constraints involved when a particle is restricted to move along a curve of surface are holonomic.

When the external magnetic field becomes greater than the internal magnetic field (magnetic field due to orbital motion + magnetic field due to spin motion) then coupling between L(orbital angular momentum) and S(spin angular momentum) is broken down. In this case L & S preceses about external magnetic field B independently. This is called paschenback effect.

The splitting of energy levels exhibited by atoms having non-zero spin is called anomalous zeeman effect. Again  the splitting of spectral line in presence of weak field is called anomalous zeeman effect.