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integration of tanz over |z|=1

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carbon nanotube.

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.

Nicol prism.

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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.

if the zero point energy of one dimensional harmonic oscillator is 5.25×10^-27 J then the energy of second excited state is

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Double pendulum.

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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.

Centre of mass coordinate system.

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.