Optionals IAS Mains Physics: Questions 286 - 292 of 306

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Question 286

Hamiltonian Lagrange's Equation from Hamilton's Principle
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Appeared in Year: 2006

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Essay▾

What is Hamilton’s Principle? Obtain Lagrange’s equation of motion from its help for a conservative system. (Marks: 25)

Explanation

Hamilton’s Principle: This principle states that for a conservative holonomic system, its motion from time to time is such that the time integral (Known as action or action integral)

Where has stationary (extremum) value for the correct path of the motion?

The quantity is called as Hamilton’s principle function.

The principle may be expressed as

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Question 287

Van Der Waals Equation of State of Real Gas
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Appeared in Year: 2015

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Short Answer▾

A Vander Waals gas undergoes Joule-Kelvin expansion with a pressure drop of 50 atm. If its initial temperature is 300K, determine its final temperature (Given Vander Waals Constant). (Marks: 10)

Question 288

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Appeared in Year: 2003

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Short Answer▾

A particle of mass m, with energy E such that, is trapped in a potential well as shown below: (Marks: 15)

Write down the time independent Schrodinger equation in region

(i)

(ii)

Question 289

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Appeared in Year: 2006

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Essay▾

What is molecular Polarizability? Derive Clausius – Mosotti equation relating the molecular polarizability with the dielectric constant of a dielectric material. (Marks: 20)

Explanation

The Polarizability, , of an atom (or molecule) is defined as the dipole moment per unit local electric field at the atom (or molecule) i. e.

Thus polarizability is an atomic (or molecular) property where as dielectric constant is a macroscopic property which depends upon the arrangement of atoms or molecules within the crystal. If all the atoms (or

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Question 290

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Appeared in Year: 2003

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Short Answer▾

Show that for at least one bound state to exist. (Marks: 30)

Question 291

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Appeared in Year: 2015

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Essay▾

Obtain Zeeman splitting for sodium D lines. (Marks: 15)

Explanation

Let us consider the Zeeman splitting of the resonance lines and of sodium. These lines arise from the transitions.

and

The Zeeman levels, g-factors and the Zeeman shifts for the various terms involved in these transitions are as follows: we know that

The Zeeman levels, g-factors and the Zeeman shifts The Zeeman levels, g-factors and the Zeeman shifts

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Question 292

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If object is placed 30 cm from a converging lens of focal length (f1) = 10 cm, find the final image position by combining the lenses as follows –

Position by combining the lenses

Position by Combining the Lenses

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Explanation

Sign convention for lens (Converging/Diverging):

Sign convention for lens (Converging/Diverging)

Sign Convention for Lens (Converging/Diverging)

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For converging lens, focal length,

For diverging lens, focal length,

* Lens formula: 1

…………………… (i)

Here,

v = image distance from pole of lens

u = object distance from pole of lens

Given,

For first lens –

(Here, sign means image formed from len

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