Solve your IGNOU Doubts

Question:

d) If the temperature of the background radiation today is $3\,K,$ at what time after the birth of the universe was the temperature $10^{15}K.$ Take the age of the universe as $15\times 10^9$ years.

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Question:

c) What is cosmic background radiation? Explain why it is so important to the debate between evolving and a steady-state universe.

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Question:

b) With the help of a diagram, explain the unified scheme for understanding active galactic nuclei.

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Question:

a) Describe Hubble’s Classification scheme for galaxies.

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Question:

d) Describe the composition of the interstellar medium. Explain how it has been possible to map the HI clouds.

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Question:

c) The mean free path of photons in stars is of the order of 0.2 cm. Show that the time taken for a photon to reach the surface of a star of radius 4 $R_e$ is of the order of one million year.

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Question:

Obtain the Taylor series expansion of $f(z)={\frac{1}{z^{2}+4}}\ \ {\mathrm{about}}\ z=-i.$

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Question:

b) Derive the expression for the mean temperature in a star:

$<T>\propto M^{2/3}<\rho >^{1/3}$

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Question:

Prove that $u=x^2-y^2$ and $v=\frac{y}{x^2+y^2}$ are harmonic functions of (x, y).

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Question:

a) Derive Jeans criteria for the stability of a gas cloud. A collapsing cloud is made only of neutral hydrogen (H1). If the temperature of the cloud is 50 K and its number

density is $10^5\,m^{-3},$ calculate its Jeans mass.

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Question:

Evaluate the integral

$\textstyle\int_{0}^{2\pi}{\frac{\sin^{2}(\theta\,\mathrm{d}\theta\,\mathrm{d}\theta\,}{5-4\,\cos\mathrm{d}}}\,$

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Question:

c) Derive an expression for the tidal force for the earth-moon system and show that its magnitude depends on the latitude. Explain tidal bulge on the basis of this expression.

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Question:

b) Explain how sunspots survive for so long even though they are surrounded by hotter matter

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Question:

a) Explain how we estimate the effective surface temperature of the Sun. A main sequence star has mass $2\times 10^{31}$ kg and radius $3\times 10^{9}$ m.Obtain an estimate of the average temperature throughout the star.

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Question:

e) The local time at Chennai is 9 p.m. Calculate the local time at Mumbai at that time.

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Question:

Show that the set of all matrices of order mn is a group under addition of matrices. Is this group abelian?

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Question:

d) Which telescope, optical or X-ray, would have higher resolving power for the same aperture? Calculate the magnitude of the faintest object that a 15 m optical telescope can detect.

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Question:

Show that velocity and acceleration are contravariant vectors.

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Question:

c) Show the horizon coordinates of a star X on a celestial sphere for a location at latitude $30^{\circ}$ N.