PHYSICS (Gravitation,Astrophysics,Magnetism &Magneto Statics)

Optional Paperâ€”1

Time : 3 Hours

Maximum Marks : 50

N.B. :â€” (1) All questions are compulsory and carry equal marks.

(2) Draw well labelled diagram wherever necessary.

**EITHER**

1. (A) Derive an expression for the gravitational potential due to a solid sphere at a point :

(i) Outside

(ii) On the surface of sphere. [5M]

(B) (i) Define Gravitational Potential and Potential energy and obtain the relation between

potential and intensity of gravitational field. [3M]

(ii) Calculate the intensity of gravitational field at a distance 0.2 m from the surface of a

solid sphere of mass 20 kg and radius 20 cm. Given G = 6.67 Ã— 10^{â€“11} Nm^{2}/kg^{2}. [2M]

**OR**

(C) Deduce an expression for gravitational self energy. [2Â½M]

(D) Calculate the gravitational energy of a galaxy if the distance between a pair of stars is

averagely 10^{20} m and composed of 1.6 Ã— 10^{11} stars of mass 2 Ã— 10^{30} each. [2Â½M]

(E) Derive an expression for the Gaussâ€™s law. [2Â½M]

(F) State and explain Newtonâ€™s law of gravitation. Define gravitation constant (G). [2Â½M]

**EITHER**

2. (A) What is Star ? Deduce an expression for the mass of the sun when a planet is orbiting in

a circular path of radius R. [5M]

(B) (i) Write short note on Asteroids and meteors. [3M]

(ii) A Star has a surface temperature of 1500Â°K. The Star will radiate its maximum energy

in what part of spectrum ?

[Given : Weinâ€™s constant b = 3 Ã— 10^{â€“3} mK] [2M]

**OR**

(C) What are Galaxies ? Give their classification. [2Â½M]

(D) Write short note on corona of Sun. [2Â½M]

(E) Explain the significance of stellar spectrum. [2Â½M]

(F) Earth receives an amount of heat radiation 1.4 Ã— 10^{3} Wm^{â€“2} from the sun. Assume the earth

re-emits all the radiation received from the Sun. Calculate the surface temperature of the earth. [2Â½M]

**EITHER**

3. (A) Explain Langevinâ€™s theory of diamagnetism and derive an expression for the magnetic

susceptibility of diamagnetic substance. [5M]

(B) (i) What is Curie-Weiss law ? Derive an expression for Curie temperature. [3M]

(ii) The magnetic susceptibility of a medium is 940 Ã— 10^{â€“4}. Calculate its absolute and

relative permeability. [2M]

**OR**

(C) What are Ferrites ? Write their applications. [2Â½M]

(D) Compare ferromagnetism and ferrimagnetism. [2Â½M]

(E) Explain the effect of temperature on antiferromagnetic material. [2Â½M]

(F) Lead in superconducting state has critical temperature of 6.2 K, at zero magnetic field and

critical field of 0.064 Am^{â€“1} at 0 K. Determine the critical field at 4 K. [2Â½M]

**EITHER**

4. (A) Deduce Ampereâ€™s circuital law. Find the expression for magnetic field due to solenoid using

Ampereâ€™s circuital law. [5M]

(B) (i) Obtain the expression for magnetic induction at a point due to a long straight conductor

carrying current I. [3M]

(ii) 20 ampere current is flowing in a long straight wire. What will be the intensity of

magnetic field at a distance 10 cm from the wire Î¼_{0} = 4Ï€ Ã— 10^{â€“7} wb/A-m. [2M]

**OR**

(C) Explain the terms :â€”

(i) Magnetization current

(ii) Magnetic field vector. [2Â½M]

(D) State Biot-Savertâ€™s Law. Obtain an expression for magnetic field intensity near a straight

conductor carrying current. [2Â½M]

(E) Deduce the relation between $Latex \overrightarrow B$ , $Latex \overrightarrow H$ and $Latex \overrightarrow M$Â [2Â½M]

(F) A circular coil of radius 5 cm has 50 turns and carries a current of 10 mA. Calculate the

magnetic induction at the centre of coil. [2Â½M]

5. Attempt any TEN :â€”Â 1Ã—10=10M

(i) Define gravitational self energy.

(ii) State Keplerâ€™s second law of planetary motion.

(iii) Calculate the force of gravitation between two bodies of masses 1 kg each and distance of

separation from their centre is 1 m (G = 6.67 Ã— 10^{â€“11} Nm^{2}/kg^{2}).

(iv) Write the sequence of planets in our solar system according to distance from Sun.

(v) Define a light year.

(vi) Give any two characteristics of star.

(vii) Give any two examples of paramagnetic material.

(viii) Define Curie temperature.

(ix) Write the formula for Bohrâ€™s magneton.

(x) Give the relation between Tesla and Gauss.

(xi) What is magnetic susceptibility ?

(xii) Draw magnetic lines of forces in a bar magnet.

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