1

This paper consists of 50 questions and Answer all the questions.

Use of calculator is not allowed.

Write your index number in the space provided in the answer sheet.

In each of the questions 1 to 50 pick one of the alternatives from (1), (2),(3),(4),(5) which is correct or most

appropriate and mark your response on the answer sheet with a cross (x) in the answer sheet.

01. A farad F (faraday) is the same as a

(1) J V-1 (2) V J-1 (3) C V-1 (4) V C-1 (5) N C-1

02. A thin ring of mass m and radius r rolls across the floor with a velocity v. Which of the following

expression would be the best estimate of the ring’s total kinetic energy as it rolls across the floor?

(1) mv2 (2) 2

2

1mv (3)

2

2

3mv (4)

r

mvmv

22

2

1 (5)

r

mvmv

22

2

1

03. Force constant k (N m-1) of a spring is actually given by an expression containing modulus of rigidity η

(N m-2), number of turns per unit length n radius of wire r, radius of spring R and length of spring l. The

correct expression for k could be

(1) Rnl

r2

4

4

η (2)

3

4

4nR

lr (3)

4

34

r

nlR

(4)

3

4

4nR

r (5) 3

4

4nlR

r

04. A liquid with coefficient of volume expansion γ is filled in a container of a material having coefficient

of linear expansion α. If the liquid overflows on heating, then

(1) γ = 3α (2) γ > 3α (3) γ < 3α (4) γ = 2α (5) γ = α3

05. The electrostatic force on a 4 μC charge at a certain position is 0.01 N. The electric field intensity at

the point will be

(1) 1 x 103 N C-1 (2) 1.5 x 103 N C-1 (3) 2 x 103 N C-1

(4) 2.5 x 103 N C-1 (5) 3 x 103 N C-1

06. The pressure and volume of saturated vapor are P and V respectively. It is compressed isothermally to

half the volume. The pressure now becomes

(1) 2 P (2) 4 P (3) P (4) 0.5 P (5) greater than P

2

07. Which of the following will make the volume of an ideal gas four times?

(1) double the absolute temperature and double the pressure.

(2) halve the absolute temperature and double the pressure.

(3) quarter the absolute temperature at constant pressure.

(4) quarter the pressure at constant temperature.

(5) quarter the absolute temperature and double the pressure.

08. The transverse nature of light is obvious by

(1) reflection. (2) refraction (3)interference. (4) diffraction (5)polarization.

09. An isolated sphere of radius R contains a uniform distribution of positive charge over the volume. Which

of the following curves correctly illustrates the dependence of the magnitude of the electric field of the

sphere as a function of the distance r from the center?

(1) (2) (3) (4) (5)

10. A solid metallic sphere is placed in a uniform electric field.

Five lines A- E are electric field lines as drawn by five

students. Which of them is correct?

(1) A (2) B (3) C (4) D (5) E

11. Equal masses of N2 and O2 gases are filled in vessels A and B at the same temperature. The volume of

vessel B is twice that of A. The ratio of pressure in vessel A and B will be (molar mass of O and N are

16 and 28 respectively.)

(1)16 : 7 (2) 16 : 14 (3) 32 : 7 (4) 32 : 28 (5) 8 : 7

12. The displacement time graph of moving particle is shown below:

The instantaneous velocity of the particle is negative at the point

(1) A (2) B (3) C (4) D (5) E

13. When a piece of paper is held with one face perpendicular to a uniform horizontal electric field the flux

through it is 25 N m2 C-1. When the paper is turned 30° from the vertical position, the flux through it is

(sin 30° = 0.50 , cos 30° = 0.87, tan 30° = 0.58)

(1) 50 N m2 C-1 (2) 28.74 N m2 C-1 (3) 21.75 N m2 C-1

(4) 14.50 N m2 C-1 (5) 12.5 N m2 C-1

14. The relative humidity of air can be decreased in spite of an increase in the absolute humidity when the

(1) Pressure raises (2) pressure falls (3) temperature rises

(4) temperature falls (5) this is impossible

3

15. If no current flows between two charged bodies when connected by a conductor,

(A) capacity (B) charge (C) potential

then which of the above must be equal ?

(1) Only (A) . (2) Only (B) . (3) Only (C) .

(4) Only (A) and (C) (5) Only (B) and (C)

16. Two objects are projected in different directions with different velocities. The path of one object with

respect to other is

(1) Parabolic (2) hyperbolic (3) eleptical (4) linear (5) circular

17. A heated objet take 4 min. to cool from 70 °C to 60 °C when the room temperature is 30 °C. The time

taken by this object to cool from 60 °C to 50 °C will be

(1) 2.8 min (2) 3.4 min (3) 4.8 min (4) 5.6 min (5) 6.2 min

18. The correct graph between the fundamental frequency f and square root of density ρ of a wire,

keeping the length, radius and tension constant, is

(1) (2) (3) (4) (5)

19. The air in a room has 12 g of water vapour. For saturation, 16 g of water vapour is required. The relative

humidity in the room is

(1) 25 % (2) 50 % (3) 60% (4) 75% (5) 95%

20. The ratio of the r.m.s. speed of the molecules of a gas and the speed of sound in an ideal gas is

(1) 1 : γ (2) 3 : γ (3) 1 : 3γ (4) 3 : (5) 1 : 3 γ

21. A particle moves from point A to point B in a gravitational field.

(A) The change of kinetic energy of the particle is equal to the potential energy change.

(B) the change of Potential energy depend on the distance between A and B.

(C) Potential energy change of the particle is independent of its mass.

Of the above statements,

(1) Only (A) is true (2) Only (C) is true (3) Only (A) and (B) are true

(4) Only (A) and (C) are true (5) All (A),(B) and (C) are False

22. Centripetal acceleration of a particle, which is moving in a circular path with a uniform angular velocity

of ω is a. The graph between ω and a is correctly represented by,

(1) (2) (3) (4) (5)

4

23. A vessel of negligible heat capacity contains 0.5 kg of water. It is heated from 25°C to 85°C by a 750

W heater in 240 s. The average rate of loss of heat to the surroundings from the vessel during this time

is (specific heat capacity of water is 4200 J K-1 kg-1)

(1) 100 W (2) 225 W (3) 275 W (4) 250 W (5) 300 W

24. Figure shows the distance time graph of an object.

Which of the following is correct?

(1) Object is moving with a uniform velocity.

(2) Object is moving with a uniform acceleration.

(3) object is moving under gravity.

(4) object is moving with acceleration starting from rest.

(5) object is moving with acceleration starting with a certain velocity.

25. A glass window conducts out heat at a certain rate when the inside temperature is 10°C and the outside

temperature is – 10 °C. The same quantity of heat will be conducted in through the window per second

when the inside temperature is 0 °C and the outside temperature is

(1) -20 °C (2) 20 °C (3) 10 °C (4) -10°C (5) -23 °C

26. A compound microscope has a magnification of 30. The focal length of the eye-piece is 3 cm. If the

final image is formed at the least distance of distinct vision (25cm), the magnification produced by the

objective is

(1) 5 (2) 7.5 (3) 10 (4) 12 (5) 8

27. A body is projected with 15 km s-1. What is its velocity in the outer space far off the earth (away from

its gravitational field)? (The escape velocity of the earth is 11 km s-1)

(1) 13 km s-1 (2) 2 13 km s-1 (3) 4 13 km s-1

(4) 8 13 km s-1 (5) 16 13 km s-1

28. Consider the following statements about the humidity.

(A) Relative humidity cannot be changed keeping absolute humidity unchanged.

(B) The dew point of a closed room/vehicle changes with the temperature in the room.

(C) In an air conditioned room, temperature as well as the relative humidity is low.

Of the above statements

(1) only (A) is true (2) only (B) is true (3) only (C) is true

(4) only (A) and (B) are true (5) only (B) and (C) are true

29. In figure, there is a charge + q at the centre of the circle ABCDE. Another charge

is placed at A. The works done in carrying a charge placed at A, in respective

path are denoted by WAB, WAC, WAD, WAE. Then which of the following is true? (1) WAE is minimum. (2) WAB is minimum.

(3) WAC is maximum (4) WAD is maximum

(5) WAB = WAC = WAD =WAE = 0

30. An illuminated object and a screen are placed at a distance D. A concex lens is brought from the object

towards the screen slowly. Then an image could be observed in two different positions of the lens. It

was found that the distance between these two positions of the lens is d. The focal length of the lens

must be

(1) 2

dD (2)

D

dD

2

2

(3)

d

dD

2

2

(4) d

dD

4

22 (5)

D

dD

4

22

5

31. Two pith balls of equal mass M and equal charge q are suspended from the same

point by a massless threads of length l as shown in the figure. For small values

of θ, the distance d between the charged pith balls at equilibrium is

(1) 3

1

2

0

2

4

1

Mg

Lq

πε (2)

3

1

2

04

1

Mg

Lq

πε (3)

2

1

2

0

2

4

1

Mg

Lq

πε

(4) 2

1

2

04

1

Mg

Lq

πε (5)

4

L

32. The figure shows a monochromatic light ray passing through a

prism. Usual symbols denote the angles as shown in the figure.

Which of the following best represent the variation of angle of

deviation d with i1 + i2

(1) (2) (3) (4) (5)

33. When a planet moves around the sun in an elliptical path,

(A) its angular momentum remains constant

(B) it moves faster when it is nearer to the sun

(C) its potential energy increases when it goes nearer to the sun

Of the above statements

(1) only (A) is true (2) only (B) is true (3) only (A) and (B) are true

(4) only (A) and (C) are true (5) all (A) , (B) and (C) are true

34. A wall has two equally thick layers A and B of different materials. The thermal conductivity of A is

thrice that of B. A temperature difference of 20°C is maintained across the wall, with the out side of A

at a higher temperature than the out side of B. Then, in steady state,

(A) the temperature difference across A is 15°C

(B) the temperature difference across A is 5°C

(C) the rate of heat transfer across A is more than that across B

(D) the rate of heat transfer across both the rods is the same

(1) only A and B are true. (2) only B and D are true. (3) only B and C are true.

(4) only A and D are true. (5) only A and C are true.

35. A foot ball is kicked from the ground at an angle 45° with the horizontal lands 32.4 m away. Which of

the following is correct about this motion if the air resistance can be neglected?

(1) It has the maximum velocity at the maximum height.

(2) The range could have been higher if it was kicked in different angle.

(3) The speed of the ball at the top of the flight is approximately 13 m s-1.

(4) There is another angle of projection to have same range.

(5) There are no other angles to project to have higher maximum height.

6

36. A satellite is moving very close to a planet of density ρ. The time period of the satellite is

(1) G

3 (2)

23

3

G

(3)

G

2

3 (4)

23

2

3

G

(5)

G

37. Two capacitors of 1 F and 2 μF are connected in series across a 100 V supply. The energy stored in

the system is

(1) 300

1J (2)

250

1 J (3)

200

1 J (4)

150

1 J (5)

100

1 J

38. A sample of an ideal gas occupies a volume V at pressure P and absolute temperature T. The mass of

each molecule is m. If k is the Boltzmann constant then the density of the gas is

(1) kT

PV (2) mkT (3)

kT

mP (4)

mP

kT (5)

kTV

P

39. Two hammers P and Q which are in the same shape and mass. Handle

of P is made of wood and that of Q is made of a metal. When it is used

to hammer a nail which one is more suitable and which position is more

suitable to handle it?

Suitable hammer suitable position to handle

(1) P A

(2) P between A and B

(3) P B

(4) Q A

(5) Q between A and B

40. A weight of specific gravity ρ is hung by the wire of the sonometer. The fundamental frequency for

transverse standing waves in the wire is 300 Hz. The weight is immersed in water so that exactly half

of its volume is submerged. The new fundamental frequency is

(1)

2

12300 (2)

12

2300

(3)

2

12300

(4)

1300 (5)

12

2300

41. Consider the following statements about thermodynamic processes

(A) In an isobaric (constant pressure) expansion no external work done by the system.

(B) In an isochoric (constant volume) process change of internal energy is proportional to the change

of temperature.

(C) In an isothermal process the change of internal energy is zero.

Of the above statements,

(1) Only (A) is true (2) Only (C) is true (3) Only (A) and (B) are true

(4) Only (B) and (C) are true (5) All (A),(B) and (C) are true

42. A ray of light passes from vacuum into a medium of refractive index n, the angle of incidence is found

to be twice the angle of refraction. Then the angle of incidence is

(1) 2

2sin 1 n (2)

2sin 1 n

(3) 2

2cos 1 n (4)

2cos 1 n

(5) n1cos

7

43. A string can withstand a tension of 100 N. 1 kg mass attached to one end of the string is whirled in a

horizontal circle keeping the free end fix. If the length of the string is 1 m, the maximum speed that can

be given to the mass is

(1) 199 m s-1 (2) 12 m s-1 (3) 99 m s-1 (4) 90 m s-1 (5) 9 m s-1

44. There is an incompressible non viscous liquid flow in the

tube shown in the figure. If the flow is a stream lined

flow, h will depend on,

(A) Density of the liquid.

(B) Rate of volume flow of liquid

(C) Cross sectional area of tube at A and B.

of the above statements.

(1) Only (A) is true. (2) Only (B) is true. (3) Only (C) is true

(4) Only (A) and (B) are true. (5) Only (B) and (C) are true.

45. A far-sighted person can see clearly up to a minimum distance of 1.0 m. Up to what minimum distance

he can see clearly with lens of power 4 D?

(1) 0.1m (2) 0.2 m (3) 0.4 m (4) 0.5 m (5) 0.8 m

46. The figure shows the variation of pressure of an ideal gass with its

density at three different temperatures T1, T2 and T3. The speed of sound

at T1, T2 and T3 are represented by v1, v2 and v3 respectively. Which of

the following statement is correct regarding the speed of sound in the

ideal gass at these temperatures?

(1) v1 < v2 < v3 (2) v1 > v2 > v3 (3) v1 > v3 > v2

(4) v1 = v2 = v3 (5) v1 < v3 < v2

47. Consider the following statements about the heat conduction.

(A) At steady state, the temperature at any point of the conductor is the same.

(B) When a solid sphere of radius R and hollow sphere of same outer radius made of same material

are heated to the same temperature and allowed to cool under same conditions, the hollow sphere

cools faster.

(C) Two thin blankets each of thickness d provide warmer covering than a single thick blanket of

same material and thickness 2d.

Of the above statements

(1) only (A) and (B) are true (2) only (A) and (C) are true

(3) only (B) and (C) are true (4) all (A) , (B) and (C) are false

(5) all (A) , (B) and (C) are true.

8

48. Three processes of an ideal gas compose a thermodynamic cycle shown in

the PV diagram.

Process 1→ 2 takes place at constant temperature (300 K).During this

process 60 J of heat enters the system.

Process 2→3 takes place at constant volume. During this process 40 J of

heat leaves the system.

Process 3→1 is adiabatic. Temperature at 3 is 275 K.

What is the change in internal energy of the system during process 3→1?

(1) -40 J (2) – 20 J (3) 0 (4) + 20 J (5) + 40 J

49. Twenty-seven water drops of the same size are charged to the same potential. If they are combined to

form a big drop, the ratio of potential of the big drop to that of a small drop is

(1) 3 (2) 6 (3) 9 (4) 27 (5) 81

50. 10 moles of an ideal gas performs a cyclic process shown in the P-

T diagram in the figure. temperature corresponding to the process

are TA = 400 K, TB = 600 K, TC = 1200 K, TD = 800 K (universal

gas constant R = 8.3 J mol-1 K-1) The net work done by the gass

during the process

(1) 0.83 kJ (2) 1.2 kJ (3) 1.66 kJ

(4) 8.3 kJ (5) 16.6 kJ

1

This paper consists of two parts A and B allowed time for both parts is 3 (three) hours.

Answer all the questions of part A on this paper itself. You must use th given space to answer. No lengthy

answers are expected.

Part B consists of 6 questions. Answer only four of them. After the exam, attach part A and part B and hand

over to the staff.

Use of calculators is not allowed.

Part - A (Structured Essay)

(g = 10 N 𝑘𝑔−1)

01' The spherometer that use to measure the thickness of the glass plate is shown in the figure. The circular

scale is divided in to 50 parts and liner scale change 0.5mm distance when the circular scale rotate one

round.

(a) i) Write down the formulae to find the least count of the instrument.

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ii) Calculate the least count of the instrument.

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(b) i) What is the adjustment that done in the instrument before obtain a reading?

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2

ii) What is the purpose of above adjustment?

'''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''

(c) i) After doing the adjustment (b)(i) the positions of the scales is shown below.

the reading of the figure is

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ii) After placing the spherometer on the glass plate the reading is 3.65𝑚𝑚. Find the correct thickness

of the spherometer.

'''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''

(d) Following formulae can be used to measure the radius of curvature of the surface,

𝑅 = 𝑎2

6ℎ +

ℎ

2

i) If there are usual meaning for symbols, Introduce them.

'''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''

ii) Following figure shows the position of scales after placing spherometer on concave surface.

Reading is,

''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''

iii) Explain the method to find the value of 'a' in the given formulae.

''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''

''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''

iv) If a = 3 cm, Find the value of 'R'.

''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''

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02' Following figures shows the apparatus that use to verity the Newton's Cooling Law.

3

(a) Draw a diagram of experimental setup of above apparatus. Mark the water level of calorimeter.

(b) i) Which method is allowed to heat loss in this method. (Conduction, convection , radiation)

'''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''

ii) One compulsory item for this experiment is not mentioned in this list. What is it?.

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iii) What is expected by this insulating base plate?

'''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''

(c) What are the quantities that should obtain readings?

'''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''

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(d) Sketch the expected graph between above quantities. Name the axis.

(e) Write down the two quantities that are obtained from the above graph.

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(f) To obtain the one quantity of above part (e), plane mirror can be used. Briefly explain this method.

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4

(g) Sketch a graph between the two quantities that obtain from above graph. Label the axis

(h) According to the above graph, what is the relationship between two quantities?

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(i) A student says the coconut oil can be used instead of water. Give two advantages of above process.

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03' A student set a practical to determine a unknown frequency of a tuning fork by using a sonometer. a) Mention the items required for the practical.

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b) i) What is the place he should keep the vibrating tuning fork to obtain the resonance?

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ii) Give the reason.

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c)

i) Draw the required harmonic (resonance wave pattern) on the figure given above.

ii) Draw the item at the suitable place that use to identify harmonic mention above.

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d) The student measure the resonance length (𝑙) for various tensions of sonometer wire by changing

the weight (𝑀𝑔) Write the expression combining 𝑀, 𝑙, 𝑓 and mass per unit length (𝑚).

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e) i) What can be the most accurate value from lengths ′𝑙′ that obtained practically ?

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ii) Give reason for that.

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f) Below figure shows the graph create for the practical by the student.

i) Mark the two points on it that use to find the gradient of the graph.

ii) Find the gradient.

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g) Find the frequency of the tuning fork if 𝑚 = 5 x 10-3 kgm-1

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h) The student use the sonometer to find the density of metal of a cylinder. The mass of solid metal

cylinder is 3.6 kg. It is hang at the end of sonometer wire. The fundamental vibration occurred in

81.2cm length. When the cylinder fully immerse in water, the above tuning fork vibrate in

fundamental tone with a length of 74.8 cm in wire. The density of water is 1000kgm-3 '

i. Find the up thrust on the cylinder by water.

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ii. Calculate the volume of the cylinder.

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iii. What is the density of the cylinder.

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04' A group of students set the apparatus for a practical of air in the school laboratory as shown in the

figure.

a) Name A, B, C and D.

A ''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''

B '''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''

C ''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''

D '''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''

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b) The physics teacher has mentioned that two main errors occur in practical arrangement and one

equipment is not suitable for this.

i. What are the main errors?

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ii. What is the unsuitable equipment.

Equipment '''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''

reason ''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''

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iii. Draw the correct arrangement of apparatus after recognizing the errors and the equipment.

c) i. Mention the Charle's law regarding the thermodynamic temperature.

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ii. Mention the combination of proportionality for those physical quantities.

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iii. Write an expression for the air volume of tube by using internal cross section of glass tube (𝐴)

and the length of air column (𝑙) in a certain temperature.

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iv. A graph can be create to check whether, the facts are true in the law, that mention in part (C)I.

1& Derive the equation to sketch the graph.

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2) Sketch the graph.

v. If the air column in tube is 24cm at 400 𝐶 temperature, calculate the maximum length of air

column for that practical.

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9

First Term Test -2019

Physics (Grade 13) Part – B (Essay)

Answer four questions only.

05' a) Derive an expression for the static pressure at a point in a liquid. b) State Archimedes' principle and verify using relevant theories. c) A cube of side 'a' is made up of material of density 𝜎1 and a sphere of radius 𝑟 is made up of a

material of density 𝜎2 . Both of these bodies have same mass 𝑚. When these bodies are put in to

a liquid of density 𝜌 they sink in it and move to the bottom of the vessel.

i. Draw free body diagrams for the two bodies at the bottom. ii. Derive an expression for the radius 𝑟 of the sphere in terms of given quantities.

d) If 𝜎1 = 4 𝑥 103 𝑘𝑔𝑚−3 , 𝜎2 = 5 𝑥 103 𝑘𝑔𝑚−3 , 𝜌 = 103 𝑘𝑔𝑚−3 and 𝑎 = 10 𝑐𝑚 then, i. Calculate 𝑟' ii. Find up thrusts on sphere and cube. e) After placing another empty floating vessel in the above vessel of water, the two bodies are placed

in it, and then the water level of the first vessel is recorded. After that one body is taken out and

put in to the vessel containing water, then what will happen to the water level? Explain your answer

giving reasons.

06' The equation 1

𝑣+

1

𝑢=

1

𝑓 can be derived for thin lenses. After applying sign convention to it, the

common lens formula can be derived. i) State the sign convention.

ii) Applying sign convention, derive the correct lens formula considering a real image formed by a

convex lens.

iii) An illuminated object is placed 20 cm away from.

(a) Convex lens (b) Concave lens

Of focal length 15 cm. Determine nature, position and magnification of the image.

iv) The focal length (F) of a combined lens formed by two co-axial thin lenses of focal lengths 𝑓1 and

𝑓2 in contact, is given by 1

𝑓 =

1

𝑓1 +

1

𝑓2

Two thin converging lenses of focal length 15 𝑐𝑚 and 25 𝑐𝑚 are placed in contact to form a

combined lens. When an object is observed through this combined lens, the final image is formed

20 𝑐𝑚 away from the lens. The image is upright and its height is 2 𝑐𝑚. Determine position and height

of the object.

07' A body moving in an orbit around much larger and massive body is called a satellite. The moon is

the natural satellite of the earth.

Satellites can be launched from the earth's surface to circle the earth. They are kept in their orbit by

the gravitational attraction of the earth.

Artificial satellites are put in to orbit at an altitude of a few hundred kilometers. at this height the air

is extremely rarefied and the friction due to it is negligible. The satellite is carried by a rocket which

achieving the desired height, releases the satellite horizontally by imparting to it a very high velocity

so that it remains moving in a nearly circular orbit.

The velocity which is imparted to an artificial satellite a few hundred kilometers above the earth's

surface, so that it may start orbiting the earth is called the orbital velocity.

Sri Lanka's first research satellite RAAVANA-1 built by two Sri Lankan engineers was launched in

to space early morning on April 18 2019 at 2.16 a.m. in Sri Lankan time. Satellite carried to the

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international space station as cargo, aboared the Antare's rocket. Which carries to the Cygnus cargo

space craft.

The aim of RAAVANA-1 satellite is to test the reduction of orbiting speeds of satellites around the

earth. It means that the team trying to reduce the angular velocity of satellites, using magnetic

torques.

RAAVANA-1 measures 11.3 cm x 10 cm x 10 cm. It weights around 1.05 kg. The life span of the

satellite is around one and half years.

It is expected to orbit 400km away from the earth. It has deployed orbit at an inclination of 51.6

degrees with orbit tangent (horizontal), earth's radius 𝑟𝐸 = 6.4 𝑥 106𝑚, 𝑔 = 9.8 𝑚𝑠−2

𝐺 = 6.67𝑥1011 𝑁𝑚2𝑘𝑔−2 i) a. What is the force that helps to keep a satellite in it's orbit? b. Describe orbital velocity?

ii) a. Consider a satellite of mass m which just circles the earth of mass M close to it's surface in an orbit.

Take 𝑟𝐸 as the radius of the earth. Write an expression for the centripetal force. b. Derive as expression to find the velocity of 𝑚 in its orbit. c. What is the velocity of m in the orbit near to the earth surface. iii) a. Suppose R is the radius of a required orbit. Write an expression to find the orbital velocity for this

orbit. b. Find the orbital velocity of RAAVANA-1. iv) a. Find vertical component of velocity when the satellite just enters into orbit.

b. Find vertical and horizontal momenta at that time. c. Calculate the magnitude of the impulse required, to enter the satellite in to orbit.

v) a. If 𝑇 is the period of satellite in it's orbit. Show that 𝑇2 = 4𝜋2 𝑅3

𝑔𝑟𝐸 2 '

b. Find the periodic time of RAAVANA-1 . c. Is RAAVANA-1 . a geostationary satellite? Give the reason for your answer. d' How many times RAAVANA-1 would orbit around the earth?

08' 1) fruit juice of different quantities are filled

with three identical containers of heat

capacity 95 𝐽𝐾−1 " 100𝑔 of ice at 00C is

added to the three containers. Assume that

when the ice is melt, there is no change of

Quality of mixture.

three containers with juice are at 300C of room temperature. Specific latent heat of ice is, 3.3 𝑥 105𝐽𝑘𝑔−1 and specific heat capacity of fruit juice is 4200 𝐽𝑘𝑔−1 𝐾−1 .

a) 200g of juice is added to the first container. It seems that total ice is not dissolved. Assume there is

no heat exchange with surrounding. i. Explain the reason for above incident. ii. Find the mass of melted ice. b) The fruit juice is just sufficient to dissolve the total ice in the second container. Find the mass of fruit

juice. c) If the third container, contain 400g of fruit juice, Find the final temperature of the mixture.

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2. The mixture of ice and water is contained in a

container having a negligible heat capacity when

the heater 100𝑤 is operated in the container,

the variation of temperature (𝜃) versus time (𝑡)

can be represented by the following graph.

a) i. What is the initial temperature of the system? ii. What is the final temperature of the system? iii. find the time taken to melt the total ice in the container. b) At the instant, the heater start to operate, find the mass of the ice in the mixture. (Specific latent heat

of ice is 3𝑥105𝐽𝑘𝑔−1 ) c) i. Find the time taken to start the vaporization of water at 00C with melted ice. ii. Find the total mass of mixture of ice and water. (Specific heat capacity of water 4200 𝐽𝐾𝑔−1𝐾−1 ) d) Find the specific latent heat of vaporization of water.

Answer either part (A) or part (B) only.

09' A) a) i) Write down the formulae to find the rate of flow of heat through a conducting rod and

introduce the terms. ii) Two rods of length 𝑙1 and 𝑙2 are connected as shown in the figure.

The thermal conductivities of two rods are 𝑘1 and 𝑘2 respectively. If the heat flow of the

combined rod is steady, show that, 𝑙1 + 𝑙2

𝐾 =

𝑙1

𝐾1 +

𝑙2

𝐾2 𝐾 is the thermal conductivity of

combined rod.

iii) If the rod is well lagged and when the system is at steady state. Show that temperature of

the interface 𝜃,

𝜃 = 𝐾1𝑇1𝑙2 + 𝐾2𝑇2𝑙1

𝐾2𝑙1 + 𝑙2𝑘1

b) Three rods of length 50 𝑐𝑚 , 100𝑐𝑚 , 150 𝑐𝑚 are connected series. The Thermal

conductivities of rods are 20, 25 , 30 𝑤𝑚−1𝑘−1 respectively. One end of the combined rod is

immersed in boiling water and other is immerse in ice at 0 C0. Find the mass of melting ice in

one hour period. Area of the crossection of rod is 10 𝑐𝑚2 and the specific latent heat of fusion

of ice is 3.3 𝑥 105𝐽𝑘𝑔−1. B) i. Write-down the biot-sharvat law and obtain and expression for magnetic flux density at a point using

above law.

ii. Obtain an expression for the magnetic flux

density at centre of the circular coil of

radius 'a' and current passing through it is 𝐼 . Consider the number of turns in the coil

is 𝑁.

12

Use the following data to answer the following questions.

Permeability of vacuum 𝜇0 = 4𝜋 𝑥 10−7𝐻/𝑚.

acceleration due to gravity g = 10 𝑚𝑠−2

A student sets up the above apparatus to measure current. Coli 𝑋 is a 100 turn circular coil of mean

diameter 300𝑚𝑚. Square coil Y, also of 100 turns, is pivoted at the center of Coil 𝑋 and is free to

turn about a horizontal axis 𝐴𝐴′ in the plane of coli 𝑋. When there is no current, the rider is adjusted

to make the pointer horizontal.

Coils X and Y are connected in series. When a current 𝐼 flows through the coils the rider has to be

moved 80𝑚𝑚 to the upward to restore the pointer to a horizontal position. a. Indicate the direction of the field produced by coil X at its when a current 𝐼 flows in the direction

shown. Determine the magnetic field B at the center of 𝑋. b. In which direction should the current in Coil 𝑌 be flowing?

Indicate the current direction and the corresponding

directions of the acting on the 4 sides of Coil 𝑌 in the digram

below. c. If the mass of the rider is 40 mg and Coil 𝑌 is of side 30mm, estimate the value of the current 𝐼,

assuming that the magnetic field due to coil X is uniform across the coil 𝑌.

Answer either part (A) or part (B) only.

10 A) a. Define angular magnification (M) of an astronomical telescope. b. Draw a ray diagram for the normal adjustment of astronomical telescope.

i. Label objective lens and eyepiece. ii. Mark 𝛼′ and 𝛼 on the diagram. iii. Mark accurate position of the image formed by the objective lens. iv. draw position of the eye. What is the special term used to name that position? c. The focal lengths of objective and eyepiece of the telescope are 50 𝑐𝑚 and 5 𝑐𝑚 respectively. When

it is in normal adjustment, what is the magnifying power of it? Calculate the separation of the lenses.

If the diameter of the objective lens is 5 𝑐𝑚 determine the diameter of the eye ring.

B) Electric field intensity of a point from a point charge at 𝑟 distance apart is, 𝐸 = 𝑘𝑞

𝑟2

i. What is the unit of 𝐸 ? ii. An electric field of 300 𝑉𝑚−1 directed to center of earth located near earth surface. a dust

particle with 8 𝑥 10−19 𝐶 charge is in stationary at a point under gravitational and electrical

forces. The gravitational field intensity of the point is 10 𝑚𝑠−2. Calculate the mass of dust

particle. iii. A proton enter to an uniform electric field of 𝐸 = 5 𝑥 105 𝑁𝐶−1. Mass of proton

𝑚 = 1.67 𝑥 10−27 𝑘𝑔. charge 𝑞 = 1.6 𝑥 10−19𝐶. a) Find out the magnitude and the direction of force act on proton inside electric field. b) Find the acceleration of proton in electric field.

iv. charges of +3.6 𝑛𝑐 and −3.6 𝑛𝑐 are placed on A and B points 5.0 𝑐𝑚 apart respectively.

A point 'P' has the separations as, A to P and B to P are 3.0 𝑐𝑚 and 4.0 𝑐𝑚.

a) Calculate, electric field at point 𝑃. b) Calculate electric potential at point 𝑃.