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) mv 2 (2) 2 2 1 mv (3) 2 2 3 mv (4) r mv mv 2 2 2 1 (5) r mv mv 2 2 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) R nl r 2 4 4 η (2) 3 4 4nR lr (3) 4 3 4 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 = α 3 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 10 3 N C -1 (2) 1.5 x 10 3 N C -1 (3) 2 x 10 3 N C -1 (4) 2.5 x 10 3 N C -1 (5) 3 x 10 3 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
32
Embed
Use of calculator is not allowed. ), (2),(3),(4),(5) which ...
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
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
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 '''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''
7
b) The physics teacher has mentioned that two main errors occur in practical arrangement and one
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
10
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
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.
11
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.