CBSE Assistant Secretary 2024: Assistant Secretary, CBSE Recruitment Examination, Tier 2 (RAS-1124), Academics and Training, Physics
Text of page 1
M A S T E R C O P Y
No. of Printed Pages : 12
RAS-1124 •ŸÈ∑˝§◊Ê¥∑§
Roll No.
ATS
Physics / ÷ÊÒÁÃ∑§‡ÊÊSòÊ
Question Paper / ¬˝‡Ÿ-¬òÊ
Time allowed : Three Hours Maximum Marks : 320
‚◊ÿ — ÃËŸ ÉÊ¥≈U •Áœ∑§Ã◊ •¥∑§ — 320
Question Paper may be detached which can be taken away by the candidate after examination.
¬˝‡Ÿ-¬òÊ •‹ª (ÁflÿÊíÿ) Á∑§ÿÊ ¡Ê ‚∑§ÃÊ „Ò •ÊÒ⁄U ¬⁄UˡÊÊÕ˸ ¬⁄UˡÊÊ ∑§ ©¬⁄Uʥà •¬Ÿ ‚ÊÕ ‹ ¡Ê ‚∑§Ã „Ò¥–
Part ‘A’ / π¥«U “•”
Part ‘A’ has 15 questions. All questions are compulsory. Each question carries 2 marks.
π¥«U “•” ◊¥ 15 ¬˝‡Ÿ „Ò¥, ÿ ‚÷Ë ¬˝‡Ÿ •ÁŸflÊÿ¸ „Ò¥– ¬˝àÿ∑§ ¬˝‡Ÿ 2 •¥∑§ ∑§Ê „Ò–
p2
1. Lagrangian of a system is given by L = − V . (Symbols have their usual meaning). The
2m
p2
corresponding Hamiltonian will be given by H = +V :
2m
(1) Only for conservative system
(2) Only for dissipative system
(3) Only for relativistic system
(4) Only for classical system
2
Á∑§‚Ë ÁŸ∑§Êÿ ∑§ Á‹∞ ‹Òª˝¥Á¡ÿŸ (Lagrangian) L = p − V mÊ⁄UÊ ÁŒÿÊ ªÿÊ „Ò– (¬˝ÃË∑§Ê¥ ∑§ ‚Ê◊Êãÿ •Õ¸ „Ò¥)– ‚¥ªÃ
2m
2
„Á◊À≈UÊÁŸÿŸ (Hamiltonian) H = p + V ÁŸêŸÁ‹Áπà ◊¥ ‚ Á∑§‚ ÁŸ∑§Êÿ ∑§ Á‹∞ ÁŒÿÊ ¡Ê ‚∑§ÃÊ „Ò?
2m
(1) ∑§fl‹ M§Á…∏flÊŒË ÁŸ∑§Êÿ ∑§ Á‹∞
(2) ∑§fl‹ •¬√ÿÿË ÁŸ∑§Êÿ ∑§ Á‹∞
(3) ∑§fl‹ ‚ʬˇÊflÊŒË ÁŸ∑§Êÿ ∑§ Á‹∞
(4) ∑§fl‹ Ä‹ÊÁ‚∑§Ëÿ ÁŸ∑§Êÿ ∑§ Á‹∞
2. The wave function of a free particle is ψ(x)=eikx. The probability current density is :
∞∑§ ◊ÈÄà ∑§áÊ ∑§Ê Ã⁄¥Uª $»¥§Ä‡ÊŸ (wave function) ψ(x)=eikx „Ò– ß‚∑§Ê ¬˝ÊÁÿ∑§ÃÊ œÊ⁄UÊ ÉÊŸàfl ÄÿÊ „Ò?
ℏk 2 ℏk k 2
(1) 0 (2) ψ (3) (4) ψ
m m m
RAS-1124 / ATS 1 Physics
Text of page 2
M A S T E R C O P Y
3. Match the Table - I with the Table - II and find the correct answer using the code given below the
tables.
Table - I Table - II
(Event) (Year)
(P) Testing of First Fission Bomb (i) 1955
(Q) Discovery of π meson (ii) 1952
(R) Testing of First Thermonuclear (iii) 1945
Bomb
(S) Discovery of Antiproton (iv) 1947
ÃÊÁ‹∑§Ê - I ∑§Ê ÃÊÁ‹∑§Ê - II ‚ ‚È◊Á‹Ã ∑§⁄¥U ÃÕÊ ÃÊÁ‹∑§Ê•Ê¥ ∑§ ŸËø ÁŒ∞ ª∞ ∑§Ê«U ∑§Ê ©¬ÿʪ ∑§⁄U∑§ ‚„Ë ©ûÊ⁄U ôÊÊà ∑§⁄¥U–
ÃÊÁ‹∑§Ê - I ÃÊÁ‹∑§Ê - II
(ÉÊ≈UŸÊ) (fl·¸)
(P) ¬„‹ Á»§$¡Ÿ ’◊ ∑§Ê ¬⁄UˡÊáÊ (i) 1995
(Q) π ◊‚Ÿ ∑§Ë πÊ¡ (ii) 1952
(R) ¬„‹ Õ◊ʸãÿÈÁÄ‹ÿ⁄U ’◊ ∑§Ê ¬⁄UˡÊáÊ (iii) 1945
(S) ∞¥≈Uˬ˝Ê≈UÊÚŸ ∑§Ë πÊ¡ (iv) 1947
Code / ∑§Ê«U :
(P) (Q) (R) (S)
(1) (i) (ii) (iii) (iv)
(2) (iv) (iii) (ii) (i)
(3) (iii) (iv) (ii) (i)
(4) (iv) (iii) (i) (ii)
4. Which one of the following has the hexagonal crystal structure ?
(1) Graphite (2) Diamond (3) Copper (4) Sodium Chloride
ÁŸêŸÁ‹Áπà ◊¥ ‚ Á∑§‚∑§Ë Á∑˝§S≈U‹ ‚¥⁄UøŸÊ ·≈˜U∑§ÊáÊËÿ (hexagonal) „ÊÃË „Ò?
(1) ª˝»§Êß≈U (2) „Ë⁄UÊ (3) ÃÊ¥’Ê (∑§Ê¬⁄U) (4) ‚ÊÁ«Uÿ◊ Ä‹Ê⁄UÊß«U
5. In which of the following Bravais lattices, all unit cell lengths (axial distances) are same but the
interaxial angles are not right angles ?
(1) Tetragonal (2) Triclinic (3) Rhombohedral (4) Orthorhombic
ÁŸêŸÁ‹Áπà ◊¥ ‚ Á∑§‚ ’˝ÊÁfl‚ ¡Ê‹∑§ (Bravais lattices) ◊¥ ‚÷Ë ß∑§Ê߸ ∑§ÊÁ‡Ê∑§Ê ‹¥’Ê߸ÿÊ° (•ˇÊËÿ ŒÍ⁄UË) ‚◊ÊŸ „Ò¥ ‹Á∑§Ÿ
•¥Ã⁄UÊˇÊËÿ ∑§ÊáÊ ‚◊∑§ÊáÊ Ÿ„Ë¥ „Êà „Ò¥?
(1) ≈U≈˛Uʪʟ‹ (2) ≈˛UÊßÁÄ‹ÁŸ∑§ (3) ⁄UÊê’Ê„«˛U‹ (4) •ÊÚÕʸ⁄UÊÁê’∑§
6. The half-life of an excited state of an atom is 8 ns. It can be assumed that it is the uncertainty in
measuring the time for photon emission. For a radiation of 500 nm, find the value of ∆v/v. (Symbols
have their usual meaning).
Á∑§‚Ë ¬⁄U◊ÊáÊÈ ∑§Ë ©ûÊÁ¡Ã •flSÕÊ ∑§Ë •œÊ¸ÿÈ 8 ns „Ò– ÿ„ ◊ÊŸÊ ¡Ê ‚∑§ÃÊ „Ò Á∑§ ÿ„ »§Ê≈UÊÚŸ ©à‚¡¸Ÿ ∑§ ‚◊ÿ ∑§Ê ◊ʬŸ ◊¥
•ÁŸÁ‡øÃÃÊ „Ò– 500 nm ∑§ ÁflÁ∑§⁄UáÊ ∑§ Á‹∞, ∆v/v. ∑§Ê ◊ÊŸ ôÊÊŸ ∑§⁄¥U– (¬˝ÃË∑§Ê¥ ∑§ •¬Ÿ ‚Ê◊Êãÿ •Õ¸ „Ò¥)–
7. The two functions that a transistor may perform in an electric circuit are : __________ and
__________.
Á∑§‚Ë ÁfllÈà ¬Á⁄U¬Õ ◊¥ ≈˛UÊ¥Á¡S≈U⁄U mÊ⁄UÊ ÁŸc¬ÊÁŒÃ Á∑§ÿ ¡ÊŸ flÊ‹ ŒÊ ∑§Êÿ¸ __________ ÃÕÊ __________„Ê ‚∑§Ã „Ò¥–
RAS-1124 / ATS 2 Physics
Text of page 3
M A S T E R C O P Y
8. The divergence of a stress tensor is a :
(1) Vector quantity (2) Scalar quantity (3) Always zero (4) Always unity
S≈˛U‚ ≈¥U‚⁄U ∑§Ê «UÊßfl⁄U¡ã‚ ∞∑§ —
(1) ‚ÁŒ‡Ê ⁄UÊÁ‡Ê „Ò (2) •ÁŒ‡Ê ⁄UÊÁ‡Ê (3) „◊‡ÊÊ ‡ÊÍãÿ (4) „◊‡ÊÊ ß∑§Ê߸
9. Temperature of three mole of an ideal gas is changed by 10 K through an isobaric process. If the
heat capacity at constant volume for the gas is 20 J/mole.K then compute the change in its internal
energy.
Á∑§‚Ë •ÊŒ‡Ê¸ ªÒ‚ ∑§ ÃËŸ ◊Ê‹ ∑§Ê Ãʬ◊ÊŸ ∞∑§ ‚◊ŒÊ’Ëÿ ¬˝Á∑˝§ÿÊ ∑§ ◊Êäÿ◊ ‚ 10 K ‚ ’Œ‹ ¡ÊÃÊ „Ò– ÿÁŒ ªÒ‚ ∑§ Á‹∞
ÁSÕ⁄U •Êÿß ¬⁄U ™§c◊Ê œÊÁ⁄UÃÊ 20 J/mole.K „Ò ÃÊ ß‚∑§Ë •Ê¥ÃÁ⁄U∑§ ™§¡Ê¸ ◊¥ ¬Á⁄UfløŸ ∑§Ë ªáÊŸÊ ∑§⁄¥U–
10. An ideal gas is compressed adiabatically. If the initial temperature of the gas is 300 K, and the gas
5
is compressed to half its initial volume, the final temperature (for a monatomic gas, γ = ) is
3
approximately :
∞∑§ •ÊŒ‡Ê¸ ªÒ‚ ∑§Ê L§Œ˜œÊc◊ M§¬ ‚ ‚¥¬ËÁ«Uà Á∑§ÿÊ ¡ÊÃÊ „Ò– ÿÁŒ ªÒ‚ ∑§Ê ¬˝Ê⁄¥UÁ÷∑§ Ãʬ◊ÊŸ 300 K „Ò, •ÊÒ⁄U ªÒ‚ ∑§Ê ©‚∑§
¬˝Ê⁄¥UÁ÷∑§ •Êÿß ∑§ •Êœ Ã∑§ ‚¥¬ËÁ«Uà Á∑§ÿÊ ¡ÊÃÊ „Ò, ÃÊ •¥ÁÃ◊ Ãʬ◊ÊŸ ‹ª÷ª „Ò — [∞∑§ ¬⁄U◊ÊÁáfl∑§ (◊ÊŸÊ∞≈UÊÁ◊∑§) ªÒ‚
5
∑§ Á‹∞, γ = 3 ]
(1) 474 K (2) 600 K (3) 350 K (4) 900 K
11. Which one of the following fields may represent a steady-state scalar field ?
ÁŸêŸÁ‹Áπà ◊¥ ‚ ∑§ÊÒŸ-‚Ê ˇÊòÊ ÁSÕ⁄U •flSÕÊ flÊ‹ •ÁŒ‡Ê ˇÊòÊ ∑§Ê ¬˝ÁÃÁŸÁœàfl ∑§⁄U ‚∑§ÃÊ „Ò?
∧ ∧
(1) V(r, t)=x2yz2+y3t (2) V(r , t ) = x 2 z j+y z k
∧ ∧
(3) V(r, t)=yz 2+102x3 (4) V(r , t ) = x 2 i + y 2 k
12. A device draws gas particles from a sealed chamber in order to leave behind a partial vacuum. It
uses mechanisms like pistons, fins or lobes to displace the air. If often finds its application in
refrigeration, air conditioning and automotive industries. Though it has a simple design but it is
reliable and can handle a wide range of gases and vapours. Identify the device.
∞∑§ ©¬∑§⁄UáÊ Á∑§‚Ë ‚Ë‹’¥Œ ∑§ˇÊ ‚ ªÒ‚ ∑§áÊÊ¥ ∑§Ê πË¥øÃÊ „Ò ÃÊÁ∑§ ∑§ˇÊ ◊¥ •Ê¥Á‡Ê∑§ ÁŸflʸà ’Ÿ ‚∑§– ÿ„ flÊÿÈ ∑§Ê ÁflSÕÊÁ¬Ã
∑§⁄UŸ ∑§ Á‹∞ Á¬S≈UŸ, ¬¥π ÿÊ ‹Ê’ ¡Ò‚ Ã¥òÊ ∑§Ê ©¬ÿʪ ∑§⁄UÃÊ „Ò– ß‚∑§Ê ©¬ÿʪ •Ä‚⁄U ¬˝‡ÊËß, ∞ÿ⁄U ∑¥§«UˇÊÁŸ¥ª •ÊÒ⁄U
•ÊÚ≈UÊ◊ÊÁ≈Ufl ©lʪʥ ◊¥ Á∑§ÿÊ ¡ÊÃÊ „Ò– „Ê‹Ê°Á∑§ ß‚∑§Ê Á«U$¡Êߟ ‚⁄U‹ „Ò ‹Á∑§Ÿ ÿ„ Áfl‡fl‚ŸËÿ „Ò •ÊÒ⁄U ªÒ‚Ê¥ •ÊÒ⁄U flÊc¬Ê¥ ∑§Ë ∞∑§
ÁflSÃÎà oÎ¥π‹Ê ∑§Ê ‚¥÷Ê‹ ‚∑§ÃÊ „Ò– ©¬∑§⁄UáÊ ∑§Ë ¬„øÊŸ ∑§⁄¥U–
13. Which one of the following could be limit for the maximum angle of diffraction in a plane
transmission diffraction grating ?
ÁŸ◊Áã‹Áπà ◊¥ ‚ ∑§ÊÒŸ-‚Ë ∞∑§ ‚◊Ë ‚¥ø⁄UáÊ ÁflfløŸ ÁS‹≈U ◊¥ ÁflfløŸ ∑§ •Áœ∑§Ã◊ ∑§ÊáÊ ∑§Ë ‚Ë◊Ê „Ê ‚∑§ÃË „Ò?
(1) 08 (2) 908 (3) 458 (4) 1808
RAS-1124 / ATS 3 Physics
Text of page 4
M A S T E R C O P Y
14. Statement (I) : Manometer is used to measure hydrostatic pressure.
Statement (II) : A manometer comprises of two connected chambers of known volumes.
(1) Both the Statements (I) and (II) are correct and Statement (II) is the correct explanation of
Statement (I).
(2) Both the Statements (I) and (II) are correct but Statement (II) is not the correct explanation
of Statement (I).
(3) Statement (I) is correct but the Statement (II) is wrong.
(4) Statement (II) is correct but the Statement (I) is wrong.
∑§ÕŸ (I) : ◊ÒŸÊ◊Ë≈U⁄U ∑§Ê ©¬ÿʪ „Êß«˛UÊS≈UÁ≈U∑§ Œ’Êfl ∑§Ê ◊ʬŸ ∑§ Á‹∞ Á∑§ÿÊ ¡ÊÃÊ „Ò–
∑§ÕŸ (II) : ◊ÒŸÊ◊Ë≈U⁄U ◊¥ ôÊÊà •Êÿß ∑§ ŒÊ ¡È«∏ „È∞ ∑§ˇÊ „Êà „Ò¥–
(1) ∑§ÕŸ (I) •ÊÒ⁄U (II) ŒÊŸÊ¥ ‚„Ë „Ò¥ •ÊÒ⁄U ∑§ÕŸ (II) ∑§ÕŸ (I) ∑§Ë ‚„Ë √ÿÊÅÿÊ „Ò–
(2) ∑§ÕŸ (I) •ÊÒ⁄U (II) ŒÊŸÊ¥ ‚„Ë „Ò¥ ‹Á∑§Ÿ ∑§ÕŸ (II) ∑§ÕŸ (I) ∑§Ë ‚„Ë √ÿÊÅÿÊ Ÿ„Ë¥ „Ò–
(3) ∑§ÕŸ (I) ‚„Ë „Ò ‹Á∑§Ÿ ∑§ÕŸ (II) ª‹Ã „Ò–
(4) ∑§ÕŸ (II) ‚„Ë „Ò ‹Á∑§Ÿ ∑§ÕŸ (I) ª‹Ã „Ò–
15. As per the Rutherford’s nuclear model of atom which one of the following schematic sketches may
correctly represent N(θ ), the number of particles per unit area that reach the screen at a scattering
angle θ ?
⁄UŒ⁄U»§Ê«¸U ∑§ ¬⁄U◊ÊáÊÈ ∑§ ŸÊÁ÷∑§Ëÿ ◊ÊÚ«U‹ ∑§ •ŸÈ‚Ê⁄U ÁŸêŸÁ‹Áπà ◊¥ ‚ ∑§ÊÒŸ ‚Ê ÿÊ¡ŸÊ’Œ˜œ ⁄UπÊÁøòÊ S∑˝§ËŸ Ã∑§ ¬„È°øŸ flÊ‹
Á∑§‚Ë Á’π⁄UÊfl ∑§ÊáÊ θ ¬⁄U ¬˝Áà ß∑§Ê߸ ˇÊòÊ ◊¥ ∑§áÊÊ¥ ∑§Ë ‚¥ÅÿÊ N(θ) ∑§Ê ‚„Ë …¥ª ‚ Œ‡ÊʸÃÊ „Ò?
(1) (2)
(3) (4)
RAS-1124 / ATS 4 Physics
Text of page 5
M A S T E R C O P Y
Part ‘B’ / π¥«U “’”
Part ‘B’ has 25 questions. Out of which any 20 questions are to be answered. Each question carries
5 marks. The question may be answered in maximum 30 words.
π¥«U “’” ◊¥ 25 ¬˝‡Ÿ „Ò¥, Á¡Ÿ◊¥ ‚ Á∑§ã„Ë¥ 20 ¬˝‡ŸÊ¥ ∑§ ©ûÊ⁄U ŒŸ „Ò¥– ¬˝àÿ∑§ ¬˝‡Ÿ 5 •¥∑§ ∑§Ê „Ò– ¬˝‡Ÿ ∑§Ê ©ûÊ⁄U •Áœ∑§Ã◊
30 ‡ÊéŒÊ¥ ◊¥ ÁŒÿÊ ¡Ê ‚∑§ÃÊ „Ò–
16. A 2 m long stick appears to be contracted when moving at a relativistic speed v=0.6c. How much
is the contraction ?
∞∑§ 2 m ‹ê’Ë ∞∑§ ¿U«∏Ë ¡’ •Ê¬ÁˇÊ∑§ øÊ‹ v=0.6c ¬⁄U ø‹ÃË „Ò ÃÊ ‚¥∑ȧÁøà ¬˝ÃËà „ÊÃË „Ò– ‚¥∑ȧøŸ Á∑§ÃŸÊ „Ò?
17. A spherical shell with inner radius R1=0.5 m and outer radius R2=1 m carries a uniform charge
density σ=10−9 C/m2. Calculate the electric field at a point r=0.75 m.
•Ê¥ à Á⁄U ∑ § ÁòÊíÿÊ R1=0.5 m •ÊÒ ⁄ U ’Ê„⁄U Ë ÁòÊíÿÊ R2=1 m flÊ‹Ê ∞∑§ ªÊ ‹ Ëÿ ∑§Ê ‡ Ê ∞∑§‚◊ÊŸ •Êfl ‡ Ê ÉÊŸàfl
σ=10−9 C/m2 mÊ⁄UÊ •ÊflÁ‡Êà „Ò– Á’¥ŒÈ r=0.75 m ¬⁄U ÁfllÈà ˇÊòÊ ∑§Ë ªáÊŸÊ ∑§ËÁ¡ÿ–
1
18. Two spin particles are in a combined spin state. What is the probability of measuring a total
2
spin S=1 when the system is in a singlet state ?
1
ŒÊ ÁS¬Ÿ ∑§áÊ ∞∑§ ‚¥ÿÈÄà ÁS¬Ÿ •flSÕÊ ◊¥ „Ò– ¡’ ÁŸ∑§Êÿ ∞∑§‹ •flSÕÊ (singlet state) ◊¥ „Ê ÃÊ ∑ȧ‹ ÁS¬Ÿ S=1
2
◊ʬŸ ∑§Ë ¬˝ÊÁÿ∑§ÃÊ ÄÿÊ „Ò?
19. An operational amplifier is configured as a non-inverting amplifier with a feedback resistor
Rf=100 kΩ and an input resistor Ri=10 kΩ . Calculate the output voltage if the input voltage is
0.2 V.
Á∑§‚Ë •ÊÚ¬⁄U‡ÊŸ‹ ∞ꬋ˻§Êÿ⁄U ∑§Ê ∞∑§ ŸÊÚŸ-ߟflÁ≈ZUª ∞ꬋ˻§Êÿ⁄U ∑§ M§¬ ◊¥ ¬Á⁄UflÁøà Á∑§ÿÊ ªÿÊ „Ò Á¡‚◊¥ ∞∑§ »§Ë«U’Ò∑§
¬˝ÁÃ⁄UÊœ Rf=100 kΩ •ÊÒ⁄U ∞∑§ ÁŸfl‡ÊË ¬˝ÁÃ⁄UÊœ Ri=10 kΩ „Ò– ÿÁŒ ÁŸfl‡ÊË flÊÀ≈UÃÊ 0.2 V „Ò ÃÊ ÁŸª¸Ã (•Ê©≈U¬È≈U)
flÊÀ≈UÃÊ ∑§Ë ªáÊŸÊ ∑§⁄¥U–
20. A Carnot refrigerator operates between a temperature of 300 K and 250 K. If it removes 100 J of
heat from the cold reservoir, calculate the work input required.
∞∑§ ∑§ÊŸÊ¸≈U ⁄UÁ»˝§¡⁄U≈U⁄U 300 K ∑§ •ÊÒ⁄U 250 K Ãʬ◊ÊŸ ∑§ ’Ëø ‚¥øÊÁ‹Ã „ÊÃÊ „Ò– ÿÁŒ ÿ„ ∆¥U«U ÁŸ∑§Êÿ (reservoir) ‚
100 J ™§c◊Ê „≈UÊÃÊ „Ò, ÃÊ •Êfl‡ÿ∑§ ÁŸfl‡ÊË ∑§Êÿ¸ ∑§Ë ªáÊŸÊ ∑§⁄¥U–
21. In a spherical region of radius 2 m, the time-dependent volume charge density is given by
ρ(t)=−3t+2 C/m3. Calculate the volume current density.
Á∑§‚Ë 2 m ÁòÊíÿÊ flÊ‹ ªÊ‹Ê∑§Ê⁄U ˇÊòÊ ◊¥, ‚◊ÿ-ÁŸ÷¸⁄U •Êÿß •Êfl‡Ê ÉÊŸàfl ρ(t)=−3t+2 C/m3 mÊ⁄UÊ ÁŒÿÊ ¡ÊÃÊ „Ò–
•Êÿß œÊ⁄UÊ ÉÊŸàfl ∑§Ë ªáÊŸÊ ∑§⁄¥U–
22. What is distinction between electronic and ionic conduction ?
ß‹Ä≈˛UÊÚÁŸ∑§ •ÊÒ⁄U •ÊÿÁŸ∑§ øÊ‹Ÿ ∑§ ’Ëø ÄÿÊ •¥Ã⁄U „ÊÃÊ „Ò?
RAS-1124 / ATS 5 Physics
Text of page 6
M A S T E R C O P Y
x
23. Using the relation ∑ x + x2 + x 3 + .... = 1 − x , find the sum of the series
2 3 4
S=1+ + 2 + 3 + .... .
2 2 2
x 2 3 4
‚¥’¥œ ∑ x + x 2 + x 3 + .... = ∑§Ê ©¬ÿʪ ∑§⁄U üÊáÊË S = 1 + + 2 + 3 + .... ∑§Ê ◊ÊŸ ôÊÊà ∑§ËÁ¡∞–
1−x 2 2 2
24. In an electric LED bulb manufacturing unit, it is seen that nearly 0.5% bulbs are defective. In a
quality check, 200 bulbs are randomly picked. It may be assumed that the conditions of using
Poisson’s distribution function are valid. What are the approximate probabilities that 0, 1, and 2 of
the bulbs respectively are defective ? (The probability of x successes in n trials can be approximated
as : Pr( X = x ) = n!
p x (1 − p)n−x
x!(n − x )!
ÿÁŒ ∑§Ê߸ ß‹ÁÄ≈˛U∑§ ∞‹ß¸«UË (LED) ’À’ ÁŸ◊ʸáÊ ß∑§Ê߸ ◊¥ ÿ„ ŒπÊ ¡ÊÃÊ „Ò Á∑§ ‹ª÷ª 0.5% ’À’ ŒÊ·¬Íáʸ „Êà „Ò¥– ªÈáÊflûÊÊ
¡Ê°ø ◊¥, 200 ’À’ ÿÊŒÎÁë¿U∑§ M§¬ ‚ øÈŸ ¡Êà „Ò¥– ÿ„ ◊ÊŸÊ ¡Ê ‚∑§ÃÊ „Ò Á∑§ ¬ÊÚß‚Ÿ ∑§ ÁflÃ⁄UáÊ $»¥§Ä‡ÊŸ ∑§Ê ©¬ÿʪ ∑§⁄UŸ ∑§Ë
‡ÊÃZ flÒœ „Ò¥– ‹ª÷ª ÄÿÊ ‚¥÷ÊflŸÊ∞° „Ò¥ Á∑§ ∑˝§◊‡Ê— 0, 1, •ÊÒ⁄U 2 ’À’ ŒÊ·¬Íáʸ „Ò¥? n ≈˛UÊÿ‹ ◊¥ x ‚»§‹ÃÊ•Ê¥ ∑§Ë ‚¥÷ÊÁflÃ
¬˝ÊÁÿ∑§ÃÊ „Ò — Pr( X = x ) = n!
p x (1 − p)n−x
x!(n − x )!
1
1
25. Using a three-point formula in trapezium rule, determine the value of ∫ 2
dx .
0 1+x
1
1
‚◊‹ê’ øÃÈ÷ȸ¡ ÁŸÿ◊ (trapezium rule) ◊¥ ÃËŸ-Á’¥ŒÈ ‚ÍòÊ ∑§Ê ©¬ÿʪ ∑§⁄U ∫ 2
dx ∑§Ê ◊ÊŸ ÁŸœÊ¸Á⁄Uà ∑§⁄¥U–
0 1+x
26. What is the activity of 1 mg sample of 222
88 Ra whose half-life is 3.8 days ? The average mass of
nucleon may be taken as 1.66×10−27 kg.
88 Ra ∑§ 1 mg Ÿ◊ÍŸ ∑§Ë ‚Á∑˝§ÿÃÊ ÄÿÊ „Ò? ãÿÍÁÄ‹•ÊÚŸ ∑§Ê •ÊÒ‚Ã Œ˝√ÿ◊ÊŸ 1.66×10
3.8 ÁŒŸ •œ¸ •ÊÿÈ flÊ‹ 222 −27 kg
Á‹ÿÊ ¡Ê ‚∑§ÃÊ „Ò–
27. What is Auger Effect ?
•ÊÚª⁄U ¬˝÷Êfl ÄÿÊ „Ò?
28. What is the energy difference (in J) between the spin-up and spin-down states of a proton in a
stronger magnetic field of 2.2 tesla ? (Component of spin magnetic moment of the proton in any
direction is 8.806×10−8 eV/T.)
2.2 ≈US‹Ê ∑§ •Áœ∑§Ã⁄U ¬˝’‹ øÈ¥’Á∑§ÿ ˇÊòÊ ◊¥ ¬˝Ê≈UÊÚŸ ∑§Ë ÁS¬Ÿ-•¬ •ÊÒ⁄U ÁS¬Ÿ-«UÊ©Ÿ •flSÕÊ•Ê¥ ∑§ ’Ëø ™§¡Ê¸ •¥Ã⁄U
(J ◊¥) ÄÿÊ „Ò? (Á∑§‚Ë ÷Ë ÁŒ‡ÊÊ ◊¥ ¬˝Ê≈UÊÚŸ ∑§ ÁS¬Ÿ øÈ¥’∑§Ëÿ •ÊÉÊÍáʸ ∑§Ê ÉÊ≈U∑§ 8.806×10−8 eV/T „Ò–)
RAS-1124 / ATS 6 Physics
Text of page 7
M A S T E R C O P Y
29. In order to evacuate a 1 m3 vacuum chamber, a diffusion pump is used. The effective pumping
speed of the diffusion pump at the inlet of the chamber is 400 L/s. Assuming that the pump is
operating under ideal conditions, how long will it take to lower the pressure in the chamber from
10−3 torr to 10−6 torr ?
Á∑§‚Ë 1 m3 flÒÄÿÍ◊ øÒ¥’⁄U ∑§Ê πÊ‹Ë ∑§⁄UŸ ∑§ Á‹∞, ∞∑§ ¬˝‚Ê⁄U ¬¥¬ ∑§Ê ©¬ÿʪ Á∑§ÿÊ ¡ÊÃÊ „Ò– øÒ¥’⁄U ∑§ ߟ‹≈U ¬⁄U ¬˝‚Ê⁄U ¬¥¬
∑§Ë ¬˝÷ÊflË ¬¥Á¬¥ª ªÁà 400 L/s „Ò– ÿ„ ◊ÊŸÃ „È∞ Á∑§ ¬¥¬ •ÊŒ‡Ê¸ ¬Á⁄UÁSÕÁÃÿÊ¥ ◊¥ ∑§Ê◊ ∑§⁄U ⁄U„Ê „Ò, øÒ¥’⁄U ◊¥ Œ’Êfl ∑§Ê
10−3 torr ‚ 10−6 torr Ã∑§ ∑§◊ ∑§⁄UŸ ◊¥ Á∑§ÃŸÊ ‚◊ÿ ‹ªªÊ?
30. What is Atomic Absorption Spectroscopy ? Give two of its uses.
¬⁄U◊ÊáÊÈ •fl‡ÊÊ·áÊ (∞≈UÊÁ◊∑§ •é‚ÊÚå‡Ê¸Ÿ) S¬Ä≈˛UÊS∑§Ê¬Ë ÄÿÊ „Ò? ß‚∑§ ŒÊ ©¬ÿʪ ’ÃÊß∞?
31. A red light He-Ne laser shines on a single slit of width 0.01 mm. The obtained diffraction pattern
is seen on a screen placed at a distance of 20 cm from the slit. What would be the linear width of
the central maxima (in mm) ?
∞∑§ ‹Ê‹ ¬˝∑§Ê‡Ê flÊ‹Ê He-Ne ‹$¡⁄U 0.01 mm øÊÒ«∏Ê߸ ∑§Ë Á∑§‚Ë ∞∑§‹ ÁS‹≈U ¬⁄U ø◊∑§ÃÊ „Ò– ¬˝Êåà ÁflfløŸ ¬Ò≈UŸ¸ ÁS‹≈U ‚
20 cm ∑§Ë ŒÍ⁄UË ¬⁄U ⁄UπË ªß¸ S∑˝§ËŸ ¬⁄U ŒπÊ ¡ÊÃÊ „Ò– ∑¥§Œ˝Ëÿ ©ÁìÊc∆U ∑§Ë ⁄ÒÁπ∑§ øÊÒ«∏Ê߸ (mm ◊¥) ÄÿÊ „ʪË?
32. What are systematic errors ? Explain their origin.
√ÿflÁSÕà òÊÈÁ≈UÿÊ° (systematic errors) ÄÿÊ „Ò¥? ©Ÿ∑§Ë ©à¬ÁûÊ ∑§Ë √ÿÊÅÿÊ ∑§⁄¥U–
33. A particle moves in a rotating frame with ω=2 rad/s. Find the pseudo force acting on it if its
speed in the lab frame is v=3 m/s.
∞∑§ ∑§áÊ ω=2 rad/s ∑§ ‚ÊÕ Á∑§‚Ë ÉÊÍáʸŸ »˝§◊ ◊¥ ªÁÃ◊ÊŸ „Ò– ÿÁŒ ¬˝ÿʪ‡ÊÊ‹Ê »˝§◊ ◊¥ ß‚∑§Ë øÊ‹ v=3 m/s „Ò, ÃÊ ß‚
¬⁄U •Ê⁄UÊÁ¬Ã ¿UŒ˜◊ ’‹ ∑§Ë ªáÊŸÊ ∑§ËÁ¡ÿ–
34. In Young’s double slit experiment, the two slits are separated by d=1 mm. Find the distance
between the 2nd and 3rd bright fringes if λ=600 nm. The screen is placed at a distance 2 m from
the slit plane.
ÿ¥ª ∑§ ÁmÁ¤Ê⁄U˸ (double slit) ¬˝ÿʪ ◊¥, ŒÊ Á¤Ê⁄U˸ÿÊ¥ ∑§ ◊äÿ ŒÍ⁄UË d=1 mm „Ò– ÿÁŒ λ=600 nm „Ê ÃÊ ŒÍ‚⁄U •ÊÒ⁄U ÃË‚⁄U
©îÊfl‹ (bright) Á»˝¥§¡Ê¥ ∑§ ’Ëø ∑§Ë ŒÍ⁄UË ôÊÊà ∑§ËÁ¡ÿ– Á¤Ê⁄U˸ ∑§ Ë ‚ ¬⁄UŒ ∑§Ê 2 m ŒÍ⁄UË ¬⁄U ⁄UπÊ ªÿÊ „Ò–
35. A long, straight wire carries a current of 20 A. Find the vector potential at a point that is 5 cm
away from the wire.
Á∑§‚Ë ‹ê’ ‚Ëœ ÃÊ⁄U ◊¥ 20 A œÊ⁄UÊ ¬˝flÊÁ„à „Ê ⁄U„Ë „Ò– ÃÊ⁄U ‚ 5 cm ∑§Ë ŒÍ⁄UË ¬⁄U ‚ÁŒ‡Ê Áfl÷fl ÄÿÊ „ʪÊ?
36. Find the Fourier transform of f(t) = e−at u(t), where u(t) is the step function, and ‘a’ is a constant
quantity.
f (t)=e−at u(t) ∑§Ê »§ÊÁ⁄Uÿ⁄U ≈˛UÊ¥S»§Ê◊¸ (Fourier transform) ¬˝Êåà ∑§ËÁ¡ÿ– ÿ„Ê° u(t) S≈U¬ »¥§Ä‡ÊŸ ÃÕÊ ‘a’ ∞∑§ ÁŸÿÃÊ¥∑§
„Ò–
RAS-1124 / ATS 7 Physics
Text of page 8
M A S T E R C O P Y
37. A circuit contains a silicon diode in series with a 500 Ω resistor. The circuit is connected to an AC
voltage source V(t)=10sin(100πt)V. Assume the diode’s forward voltage is 0.7 V. Calculate the
peak current through the resistor and the diode. Also determine the power dissipitated in the
diode over one cycle.
Á∑§‚Ë ¬Á⁄U¬Õ ◊¥ ∞∑§ Á‚Á‹∑§ÊÚŸ «UÊÿÊ«U ∞∑§ 500 Ω ∑§ ¬˝ÁÃ⁄UÊœ∑§ ∑§ ‚ÊÕ üÊáÊË ∑˝§◊ ◊¥ ‚¥ÿÊÁ¡Ã „Ò– ÿ„ ¬Á⁄U¬Õ ∞∑§ AC
flÊÀ≈UÃÊ dÊà V(t)=10sin(100πt)V ∑§ ‚ÊÕ ¡È«∏Ê „Ò– ÿ„ ◊ÊŸÃ „È∞ Á∑§ «UÊÿÊ«U ∑§Ë •ª˝¡ flÊÀ≈UÃÊ (forward voltage)
0.7 V „Ò, ¬˝ÁÃ⁄UÊœ∑§ •ÊÒ⁄U «UÊÿÊ«U ‚ ¬˝flÊÁ„à „ÊŸ flÊ‹Ë Á‡Êπ⁄U œÊ⁄UÊÿ¥ (peak currents) ∑§Ë ªáÊŸÊ ∑§ËÁ¡ÿ– ∞∑§ ø∑˝§ ◊¥
«UÊÿÊ«U ◊¥ •¬√ÿÁÿà ‡ÊÁÄà ∑§Ê ÁŸœÊ¸⁄UáÊ ÷Ë ∑§ËÁ¡ÿ–
38. A blackbody at a temperature of 5000 K emits most of its radiation in the visible spectrum.
5000 K Ãʬ◊ÊŸ ¬⁄U ∑§Ê߸ ∑ΧÁcáÊ∑§Ê (blackbody) ‚ •Áœ∑§Ê¥‡Ê× ÁflÁ∑§⁄UáÊ ŒÎ‡ÿ◊ÊŸ S¬Ä≈˛U◊ ◊¥ ©à‚¡¸Ÿ „ÊÃÊ „Ò–
(a) What is the peak wavelength of the radiation emitted by the blackbody ?
∑ΧÁcáÊ∑§Ê ‚ ©à‚Á¡¸Ã ÁflÁ∑§⁄UáÊ ∑§Ë Á‡Êπ⁄U Ã⁄¥UªŒÒäÿ¸ ÄÿÊ „ÊÃË „Ò?
(b) Calculate the total energy emitted per unit area per unit time by the blackbody.
∑ΧÁcáÊ∑§Ê ‚ ¬˝Áà ß∑§Ê߸ ˇÊòÊ ¬˝Áà ß∑§Ê߸ ‚◊ÿ ◊¥ ©à‚Á¡¸Ã ∑ȧ‹ ™§¡Ê¸ ∑§Ë ªáÊŸÊ ∑§ËÁ¡ÿ–
(Use Wien’s displacement constant = 2.898×10 −3 m K ; Stefan-Boltzmann constant
= 5.67×10−8 Wm−2K−4)
flŸ ÁflSÕʬŸ ÁSÕ⁄UÊ¥∑§ (Wien’s displacement constant = 2.898×10−3 m K ; S≈UË$»§Ÿ-’ÊÀ≈˜U¡◊ÒŸ ÁSÕ⁄UÊ¥∑§
= 5.67×10−8 Wm−2K−4)
39. Consider a BJT in a common-emitter configuration with a collector supply voltage VCC = 20 V,
and a collector resistor RC=1 KΩ. The transistor has a current gain β=150 and the base-emitter
voltage VBE=0.7 V. If the base current IB is 50µA, calculate the following :
∞∑§ ∑§‹Ä≈U⁄U •Ê¬ÍÁø flÊÀ≈UÃÊ VCC = 20 V •ÊÒ⁄ ∑§‹Ä≈U⁄U ¬˝ÁÃ⁄UÊœ∑§ RC=1 KΩ ∑§ ‚ÊÕ Á∑§‚Ë ©÷ÿ-∞◊Ë≈U⁄U ÁflãÿÊ‚
(common-emitter configuration) BJT ¬⁄U ÁfløÊ⁄ Á∑§Á¡ÿ– ≈˛UÊ¥Á¡S≈U⁄U ∑§Ë œÊ⁄UÊ-‹Áéœ (current gain) β=150 „Ò
ÃÕÊ ’‚-∞◊Ë≈U⁄U flÊÀ≈UÃÊ VBE=0.7 V „Ò– ÿÁŒ ’‚-œÊ⁄UÊ IB=50µA „Ê ÃÊ ÁŸêŸ ∑§Ë ªáÊŸÊ ∑§ËÁ¡ÿ —
(a) The collector current IC.
∑§‹Ä≈U⁄U œÊ⁄UÊ IC
(b) The voltage VCE between collector and emitter.
∑§‹Ä≈U⁄U •ÊÒ⁄U ∞◊Ë≈U⁄U ∑§ ◊äÿ flÊÀ≈UÃÊ VCE
(c) Discuss the mode of operation of the transistor (active, saturation, or cut off).
≈˛UÊ¥Á¡S≈U⁄U ∑§ ‚¥øÊ‹Ÿ (‚Á∑˝§ÿ, ‚¥ÃÎåà ÿÊ •Ê¥àÿÁÃ∑§ (cut off)) ◊Ê«U ∑§Ë ÁflfløŸÊ ∑§ËÁ¡ÿ
40. Draw a schematic energy-level diagram of a solid-state laser.
Á∑§‚Ë ∆UÊ‚ÊflSÕÊ ‹¡⁄U ∑§ Á‹∞ ¬˝ÃË∑§Êà◊∑§ ™§¡Ê¸-SÃ⁄U ÁøòÊ ∑§Ê ÁŸM§¬áÊ ∑§ËÁ¡ÿ–
RAS-1124 / ATS 8 Physics
Text of page 9
M A S T E R C O P Y
Part ‘C’ / π¥«U “‚”
Part ‘C’ has 12 questions. Out of which any 10 questions are to be answered. Each question carries
10 marks. The question may be answered in maximum 100 words.
π¥«U “‚” ◊¥ 12 ¬˝‡Ÿ „Ò¥, Á¡Ÿ◊¥ ‚ Á∑§ã„Ë¥ 10 ¬˝‡ŸÊ¥ ∑§ ©ûÊ⁄U ŒŸ „Ò¥– ¬˝àÿ∑§ ¬˝‡Ÿ 10 •¥∑§ ∑§Ê „Ò– ¬˝‡Ÿ ∑§Ê ©ûÊ⁄U •Áœ∑§Ã◊
100 ‡ÊéŒÊ¥ ◊¥ ÁŒÿÊ ¡Ê ‚∑§ÃÊ „Ò–
→ ∧ ∧ → ∧
41. In rest frame, the velocities of two objects are given by v1 = 0.3c x + 0.6 c y ; and v2 =−0.6 c x .
Calculate the velocity of the first object as measured in the rest frame of the second object.
→ ∧ ∧ →
ÁflüÊÊ◊ »˝§◊ ◊¥, ŒÊ flSÃÈ•Ê¥ ∑§ flª ß‚ ¬˝∑§Ê⁄U ÁŒ∞ ª∞ „Ò¥ v1 = 0.3c x + 0.6 c y ; •ÊÒ⁄U v2 =−0.6 c x∧ ŒÍ‚⁄UË flSÃÈ ∑§
Áfl⁄UÊ◊ »˝§◊ ◊¥ ◊Ê¬Ë ªß¸ ¬„‹Ë flSÃÈ ∑§ flª ∑§Ë ªáÊŸÊ ∑§⁄¥U–
42. What is the Larmor frequency of a proton in a stronger magnetic field of 3.0 tesla ? Identify the
region of electromagnetic spectrum in which it falls. (Component of spin magnetic moment of the
proton in any direction is 8.806×10−8 eV/T).
3.0 ≈US‹Ê ∑§ •Áœ∑§Ã⁄U ¬˝’‹ øÈ¥’∑§Ëÿ ˇÊòÊ ◊¥ ¬˝Ê≈UÊÚŸ ∑§Ë ‹Ê◊ʸ⁄U •ÊflÎÁûÊ ÄÿÊ „Ò? ÁfllÈà øÈ¥’∑§Ëÿ S¬Ä≈˛U◊ ∑§ ©‚ ˇÊòÊ ∑§Ë
¬„øÊŸ ∑§⁄¥U Á¡‚◊¥ ÿ„ •ÊÃË „Ò– (Á∑§‚Ë ÷Ë ÁŒ‡ÊÊ ◊¥ ¬˝Ê≈UÊÚŸ ∑§ ÁS¬Ÿ øÈ¥’∑§Ëÿ •ÊÉÊÍáʸ ∑§Ê ÉÊ≈U∑§ 8.806×10−8 eV/T „Ò–)
43. The energy levels with increasing energy in a multiplet are separated with 3 : 5 ratio for line
spectrum of an arbitrary atom. Designate S, L and J quantum numbers to these levels via/using
Lande’s interval rule.
Á∑§‚Ë ∞Áë¿U∑§ (arbitrary) ¬⁄U◊ÊáÊÈ ∑§ ‹Êߟ S¬Ä≈˛U◊ ∑§ ◊À≈UËå‹≈U ◊¥ ’…∏ÃË ™§¡Ê¸ ∑§ ‚ÊÕ ™§¡Ê¸-SÃ⁄U 3 : 5 •ŸÈ¬Êà ∑§ ‚ÊÕ
¬ÎÕÁ∑§Ã „Ò¥– ‹Ò¥«U ∑§ •¥Ã⁄UÊ‹ ÁŸÿ◊ (Lande’s interval rule) ∑§Ê ©¬ÿʪ ∑§⁄U ߟ SÃ⁄UÊ¥ ∑§ S, L •ÊÒ⁄U J ÄflÊ¥≈U◊ ‚¥ÅÿÊ∞°
ÁŸÁŒ¸c≈U ∑§⁄¥U–
44. A Carnot engine operates between two thermal reservoirs at temperatures T H=600 K and
TC=300K. The engine absorbs QH=4000 J of heat from the hot reservoir.
Á∑§‚Ë ∑§ÊŸÊ¸ ߥ¡Ÿ ŒÊ ÃʬËÿ ÁŸ∑§ÊÿÊ¥ (reservoirs) (TH=600 K •ÊÒ⁄U TC=300K) ∑§ ◊äÿ ‚¥øÊÁ‹Ã „ÊÃÊ „Ò– ߥ¡Ÿ ª◊¸
ÁŸ∑§Êÿ ‚ QH=4000 J ™§c◊Ê •fl‡ÊÊÁ·Ã ∑§⁄UÃÊ „Ò–
(a) Calculate the work output of the engine and the heat rejected to the cold reservoir.
ߥ¡Ÿ mÊ⁄UÊ ÁŸª¸Ã ∑§Êÿ¸ ÃÕÊ ∆¥U«U ÁŸ∑§Êÿ ◊¥ ¿UÊ«∏Ë ªÿË ™§c◊Ê ∑§Ë ªáÊŸÊ ∑§ËÁ¡ÿ–
(b) Determine the change in entropy for both the hot and cold reservoirs during one cycle of the
engine.
ߥ¡Ÿ ∑§ ∑§Êÿ¸ ∑§ ∞∑§ ø∑˝§ ∑§ ŒÊÒ⁄UÊŸ ª◊¸ •ÊÒ⁄U ∆¥U«U ŒÊŸÊ¥ ÁŸ∑§ÊÿÊ¥ ∑§ Á‹∞ ∞ã≈˛UÊ¬Ë ◊¥ ¬Á⁄UfløŸ ∑§Ê ÁŸœÊ¸⁄UáÊ ∑§⁄¥U–
45. Calculate the change in entropy ∆S for one mole of an ideal gas when it is isothermally expanded
from an initial volume V1 to a final volume V2 at a temperature T. Use the relation for entropy
change in an ideal gas.
Á∑§‚Ë •ÊŒ‡Ê¸ ªÒ‚ ∑§ ∞∑§ ◊Ê‹ ∑§ Á‹∞ ∞ã≈˛UÊÚ¬Ë ∆S ◊¥ ¬Á⁄UfløŸ ∑§Ë ªáÊŸÊ ∑§⁄¥U ¡’ ß‚ Ãʬ◊ÊŸ T ¬⁄U ¬˝Ê⁄¥UÁ÷∑§ •Êÿß
V1 ‚ •¥ÁÃ◊ •Êÿß V2 Ã∑§ ‚◊ÃÊ¬Ë M§¬ ‚ ÁflSÃÊÁ⁄Uà Á∑§ÿÊ ¡ÊÃÊ „Ò– ∞∑§ •ÊŒ‡Ê¸ ªÒ‚ ◊¥ ∞ã≈˛UÊÚ¬Ë ¬Á⁄UfløŸ ∑§ Á‹∞ ‚¥’¥œ
∑§Ê ©¬ÿʪ ∑§⁄¥U–
RAS-1124 / ATS 9 Physics
Text of page 10
M A S T E R C O P Y
46. Find y(0.1) for y9=(x−y)/2, x0=0, y 0=1, with step length 0.1 using Runge-Kutta 4 method
(1st order derivative).
ø⁄UáÊ ‹¥’Ê߸ 0.1 ∑§ ‚ÊÕ Á∑§‚Ë »§‹Ÿ y9=(x−y)/2, x0=0, y0=1, ∑§ Á‹∞ y(0.1) ∑§Ê ◊ÊŸ ⁄UŸª-∑ȧ≈˜U≈UÊ 4 ÁflÁœ
(¬˝Õ◊ ∑˝§◊ √ÿÈà¬ãŸ) [Runge-Kutta 4 method (1st order derivative)] ∑§Ê ©¬ÿʪ ∑§⁄U ôÊÊà ∑§⁄¥U–
47. What is a Monochromator ? Draw a schematic diagram of a Czerny-Turner monochromator.
◊ÊŸÊ∑˝§Ê◊≈U⁄U ÄÿÊ „Ò? øŸË¸-≈UŸ¸⁄U ◊ÊŸÊ∑˝§Ê◊≈U⁄U ∑§Ê ÿÊ¡ŸÊ’Œ˜œ •Ê⁄Uπ ’ŸÊ∞°–
48. A mass m=3 kg is attached to a spring with spring constant k=150 N/m and is initially compressed
x0=0.4 m from its equilibrium position.
∞∑§=3 kg ŒÎ√ÿ◊ÊŸ ∑§Ê Á¬¥«U ∞∑§ ÁS¬˝¥ª Á¡‚∑§Ê ÁS¬˝¥ª-ÁSÕÊ⁄UÊ¥∑§ k=150 N/m „Ò ‚ ‚¥ÿÊÁ¡Ã „Ò– ¬˝Ê⁄Uê÷ ◊¥ ÿ„ •¬ŸË
‚ÊêÿflSÕÊ ‚ x0=0.4 m ‚ ‚¥¬ËÁ«Uà „Ò–
(a) Determine the frequency of the oscillation and derive the expression for the total mechanical
energy of the system when released.
ŒÊ‹Ÿ ∑§Ë •ÊflÎÁûÊ ÁŸœÊ¸Á⁄Uà ∑§⁄¥U •ÊÒ⁄U ◊ÈÄà „ÊŸ ¬⁄U ¬˝áÊÊ‹Ë ∑§Ë ∑ȧ‹ ÿÊ¥ÁòÊ∑§ ™§¡Ê¸ ∑§ Á‹∞ √ÿ¥¡∑§ ¬˝Êåà ∑§⁄¥U–
(b) If the mass is subjected to a damping force proportional to its velocity F d=−bv where
b=6 Ns/m, write the equation of motion and identify the damping ratio.
ÿÁŒ Á¬¥«U ¬⁄U ©‚∑§ ‚◊ʟȬÊÃË •fl◊¥ŒŸ ’‹ Fd=−bv „Ê, ¡„Ê° b=6 Ns/m „Ò, ÃÊ ªÁà ∑§Ê ‚◊Ë∑§⁄UáÊ ¬˝ÊåÃ
∑§ËÁ¡∞ •ÊÒ⁄U •fl◊¥ŒŸ •ŸÈ¬Êà ∑§Ë ªáÊŸÊ ∑§ËÁ¡∞–
2
49. Calculate the expectation value of the angular momentum squared L for a particle in a state
l = 1, m = 0
Á∑§‚Ë ∑§áÊ ∑§ Á‹∞ ∑§ÊáÊËÿ ‚¥flª flª¸ L2 ∑§ •¬ÁˇÊà ◊ÊŸ (expectation value) ∑§Ë ªáÊŸÊ ∑§⁄¥U, ¡Ê Á∑§ l = 1, m = 0
•flSÕÊ ◊¥ „Ê–
50. A particle moving in one dimension is in a stationary state whose wave function is given by :
0, x < −a ,
πx
ψ( x ) = A 1 + cos , −a ≤ x ≤ a ,
a
0, x > a,
Where A and a are real constants. Verify that this above wave function is valid.
Á∑§‚Ë ∞∑§-Áfl◊Ëÿ ÁŒ‡ÊÊ ◊¥ ªÁÃ◊ÊŸ ∑§áÊ ∑§Ê •ø‹ •flSÕÊ ◊¥ Ã⁄¥Uª »§‹Ÿ ÁŸêŸ „Ò —
0, x < −a ,
πx
ψ( x ) = A 1 + cos , −a ≤ x ≤ a ,
a
0, x > a,
¡„Ê° A •ÊÒ⁄U a flÊSÃÁfl∑§ ÁSÕ⁄UÊ¥∑§ „Ò¥– ‚àÿÊÁ¬Ã ∑§⁄¥U Á∑§ ÿ„ Ã⁄¥Uª $»¥§Ä‡ÊŸ flÒœ „Ò–
RAS-1124 / ATS 10 Physics
Text of page 11
M A S T E R C O P Y
51. (a) A long straight wire carries a current of I=10 A. Calculate the magnetic field at a distance
of 0.05 m from it.
Á∑§‚Ë ‹¥’ ‚Ëœ ÃÊ⁄U ◊¥ I=10 A œÊ⁄UÊ ¬˝flÊÁ„à „Ê ⁄U„Ë „Ò– ÃÊ⁄U ‚ 0.05 m ∑§Ë ŒÍ⁄UË ¬⁄U øÈ¥’∑§Ëÿ ˇÊòÊ ∑§Ë ªáÊŸÊ ∑§ËÁ¡∞–
(b) A steady current I=10 A flows through a circular loop of radius 0.05 m. What is the magnetic
field at the centre of the loop.
0.05 m ÁòÊíÿÊ ∑§Ë ∞∑§ flÎûÊÊ∑§Ê⁄U ‹Í¬ ◊¥ ∞∑§ ÁŸÿà œÊ⁄UÊ I=10 A ¬˝flÊÁ„à „Ê ⁄U„Ë „Ò– ‹Í¬ ∑§ ∑§ãŒ˝ ¬⁄U øÈ¥’∑§Ëÿ ˇÊòÊ
ÄÿÊ „ʪÊ?
(c) Compare the magnetic fields obtained in parts (a) and (b).
(a) •ÊÒ⁄U (b) ◊¥ ¬˝Êåà øÈ¥’∑§Ëÿ ˇÊòÊ ∑§Ë ÃÈ‹ŸÊ ∑§ËÁ¡ÿ–
52. An operational amplifier is configured as a non-inverting amplifier with feedback resistor
Rf=20 kΩ and input resistor Rin=5 kΩ. The input voltage is Vin=2 V.
∞∑§ •ÊÚ¬⁄U‡ÊŸ - ‚¥flœ¸∑§ (amplifier) ∑§Ê ∞∑§ »§Ë«U’Ò∑§ ¬˝ÁÃ⁄UÊœ∑§ Rf=20 kΩ •ÊÒ⁄U ÁŸfl‡ÊË ¬˝ÁÃ⁄UÊœ∑§ Rin=5 kΩ ∑§
‚ÊÕ ŸÊÚŸ-ߥŸflÁ≈ZUª ‚¥flœ¸∑§ ∑§ M§¬ ◊¥ ‹ªÊÿÊ ªÿÊ „Ò– ÁŸfl‡Ê flÊÀ≈UÃÊ Vin=2 V „Ò —
(a) Calculate the gain of the amplifier and the output voltage Vout.
‚¥flœ¸∑§ ∑§Ë ‹Áéœ (gain) •ÊÒ⁄U ÁŸª¸Ã flÊÀ≈UÃÊ (Vout) ∑§Ë ªáÊŸÊ ∑§ËÁ¡ÿ–
(b) If a load of 10 kΩ is connected to the output, determine the voltage across the load and
discuss the effect of loading on the output voltage.
ÿÁŒ ÁŸª¸Ã ‚ 10 kΩ ∑§Ê ‹Ê«U ¡È«∏Ê „È•Ê „Ò ÃÊ ‹Ê«U ¬⁄U flÊÀ≈UÃÊ ÁŸœÊ¸Á⁄Uà ∑§⁄¥U •ÊÒ⁄U ÁŸª¸Ã flÊÀ≈UÃÊ ¬⁄U ‹ÊÁ«U¥ª ∑§ ¬˝÷Êfl
∑§Ë √ÿÊÅÿÊ ∑§⁄¥U–
Part ‘D’ / π¥«U “Œ”
Part ‘D’ has 5 questions. Out of which any 3 questions are to be answered. Each question carries
30 marks. The question may be answered in maximum 300 words.
π¥«U “Œ” ◊¥ 5 ¬˝‡Ÿ „Ò¥, Á¡Ÿ◊¥ ‚ Á∑§ã„Ë¥ 3 ¬˝‡ŸÊ¥ ∑§ ©ûÊ⁄U ŒŸ „Ò¥– ¬˝àÿ∑§ ¬˝‡Ÿ 30 •¥∑§ ∑§Ê „Ò– ¬˝‡Ÿ ∑§Ê ©ûÊ⁄U •Áœ∑§Ã◊
300 ‡ÊéŒÊ¥ ◊¥ ÁŒÿÊ ¡Ê ‚∑§ÃÊ „Ò–
53. Consider a system with generalized coordinates q and conjugate momenta p. The Hamiltonian is
2
given by H (q , p ) = p + 1 kq 2 . Compute the Poisson bracket {q2, p2} and evaluate it at q = 1 m
2m 2
and p = 2 kg m/s.
2
‚Ê◊ÊãÿË∑Χà ÁŸŒ¸‡ÊÊ¥∑§ q •ÊÒ⁄U ‚¥ÿÈÇ◊ ‚¥flª p flÊ‹Ë ¬˝áÊÊ‹Ë ¬⁄U ÁfløÊ⁄U ∑§⁄¥U– „ÒÁ◊À≈UÊÁŸÿŸ H (q , p) = p +
1 2 mÊ⁄UÊ
kq
2m 2
ÁŒÿÊ ªÿÊ „Ò– ¬ÊÚß‚Ÿ ’Ò˝∑§≈U {q2, p2} ∑§Ë ªáÊŸÊ ∑§⁄¥U •ÊÒ⁄U ß‚ q = 1 m •ÊÒ⁄U p = 2 kg m/s ¬⁄U ◊ÍÀÿÊ¥Á∑§Ã ∑§⁄¥U–
RAS-1124 / ATS 11 Physics
Text of page 12
M A S T E R C O P Y
54. A photon is emitted by an excited hydrogen atom when an electron jumps from n = 10 to the
ground state. [Given Rydberg constant = 1.097×107 m−1, h=6.63×10−34 Js, c=3×108 m/s
and mass of proton = 1.67×10−27 kg]
∞∑§ ß‹Ä≈˛UÊÚŸ n = 10 ‚ ◊Í‹ (ground) •flSÕÊ ◊¥ •ÊŸ ¬⁄U Á∑§‚Ë ©ûÊÁ¡Ã „Êß«˛UÊ¡Ÿ ¬⁄U◊ÊáÊÈ mÊ⁄UÊ ∞∑§ »§Ê≈UÊÚŸ ©à‚Á¡¸Ã
„ÊÃÊ „Ò–
[ÁŒÿÊ ªÿÊ „Ò Á⁄U«U’ª¸ ÁSÕ⁄UÊ¥∑§ = 1.097×107 m−1, h=6.63×10−34 Js, c=3×108 m/s •ÊÒ⁄U ¬˝Ê≈UÊÚŸ ∑§Ê Œ˝√ÿ◊ÊŸ
= 1.67×10−27 kg]
Find / ÁŸêŸ ∑§Ë ªáÊŸÊ ∑§ËÁ¡∞ —
(a) Energy of the photon
»§Ê≈UÊÚŸ ∑§Ë ™§¡Ê¸
(b) Momentum of the photon
¬Ê≈UÊÚŸ ∑§Ê ‚¥flª
(c) Wavelength of the photon
»§Ê≈UÊÚŸ ∑§Ë Ã⁄¥Uª ŒÒäÿ¸
(d) Recoil speed of the hydrogen atom
„Êß«˛UÊ¡Ÿ ¬⁄U◊ÊáÊÈ ∑§Ë ¬˝ÁÃˇÊ¬ ªÁà (Recoil speed)
55. Consider a region in space with a potential V(r) satisfying Laplace’s equation ∇2V=0 for r > a
(Where r = r ) and the boundary condition that V→0 as r→∞. Inside a sphere of radius a, the
potential is given by : V (r ) = Ar + B , for r ≤ a.
r2
Determine the constants A and B if it is known that the electric field E is zero at the center of the
sphere (r=0) and the potential V(a)=V0.
S¬‡Ê ◊¥ Á∑§‚Ë ∞∑§ ˇÊòÊ ¬⁄U ÁfløÊ⁄U ∑§⁄¥U Á¡‚◊¥ Áfl÷fl V(r) „Ò ¡Ê r > a (¡„Ê° r = r ); ÃÕÊ ‚Ë◊Ê ‡Êø V→0 ÿÁŒ r→∞∑§
Á‹∞ ‹Êå‹Ê‚ ‚◊Ë∑§⁄UáÊ ∇2V=0 ∑§Ê ‚¥ÃÈc≈U ∑§⁄UÃÊ „Ò–
ÁòÊíÿÊ a ∑§ ∞∑§ ªÊ‹ ∑§ ÷ËÃ⁄ Áfl÷fl
B
V (r ) = Ar + 2 , for r ≤ a.
r
‚ ÁŒÿÊ ¡ÊÃÊ „Ò– ÿÁŒ ÿ„ ôÊÊà „Ò Á∑§ ªÊ‹ ∑§ ∑¥§Œ˝ (r=0) ¬⁄U ÁfllÈà ˇÊòÊ E ‡ÊÍãÿ „Ò •ÊÒ⁄U Áfl÷fl V(a)=V0 „Ò, ÃÊ ÁSÕ⁄UÊ¥∑§
A •ÊÒ⁄U B ÁŸœÊ¸Á⁄Uà ∑§⁄¥U–
56. (a) How does the electron structure of an isolated atom differ from that of a solid material ?
Á∑§‚Ë ¬ÎÕ∑§ ¬⁄U◊ÊáÊÈ ◊¥ ß‹Ä≈˛UÊÚŸ ‚¥⁄UøŸÊ, Á∑§‚Ë ∆UÊ‚ ¬ŒÊÕ¸ ∑§Ë ß‹Ä≈˛UÊÚŸ ‚¥⁄UøŸÊ ‚ Á∑§‚ ¬˝∑§Ê⁄U Á÷㟠„ÊÃË „Ò?
(b) In terms of electron energy band structure, discuss reasons for the difference in electrical
conductivity between metals, semiconductors and insulators.
ß‹Ä≈˛UÊÚŸ ™§¡Ê¸ ’Ò¥«U ‚¥⁄UøŸÊ ∑§ ‚¥Œ÷¸ ◊¥, œÊÃÈ•Ê¥, •œ¸øÊ‹∑§Ê¥ •ÊÒ⁄U ∑ȧøÊ‹∑§Ê¥ ◊¥ ÁfllÈà øÊ‹∑§ÃÊ ∑§ •¥Ã⁄U ∑§ ∑§Ê⁄UáÊÊ¥
∑§Ë √ÿÊÅÿÊ ∑§⁄¥U–
57. Write short notes on following :
ÁŸêŸÁ‹Áπà ¬⁄U ‚¥ÁˇÊåà Á≈Uå¬ÁáÊÿÊ° Á‹π¥ —
(a) Quarks (b) Leptons (c) Bosons (d) Isospin (e) Spin
ÄflÊ∑¸§ ‹å≈UÊÚŸ ’Ê‚ÊÚŸ •Êß‚ÊÁS¬Ÿ ÁS¬Ÿ
-o0o-
RAS-1124 / ATS 12 PhysicsOfficial key not published for this paper.
Page 1 of 12
Source: Central Board of Secondary Education. Question paper published by Central Board of Secondary Education.