S6 Physics 2007
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Physics I
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07 Nov. 2007
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RWANDA NATIONAL EXAMINATIONS COUNCIL
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P.O.BOX 3817 KIGALI-TEL/' FAX : 586871 Y
ADVANCED LEVEL NATIONAL EXAMINATION 2007 SUBJECT
: PHYSICS I
OPTION
: MATHEMATICS-PHYSICS
TIME
21-»
: 3 HOURS
1 V
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INSTRUCTIONS:
Thispaper consists of THREE Sections A, B and C.
.‘
Section A: Attempt ALL 15 questions. (55 marks) Section B: Attempt any THREE questions. (36 marks) Section C: Attempt ONE question only. [15 marks) Yourggay use the following information if needed. Speed oT'ligh't in a vacuum or in air c= 3x 108m/s Speed of sound in air = 345m /s. Acceleration due to gravity g =9.80m/ s2. Planckfs constant h = 6.63 X lO"34 J.S. Permittivity of free space so = 8.852110-12 C2/N.m2 - / Permeability of free space no = 41: x 10-7 Wb]A.m2 Universal constant of gases R = 8-31 F]/mol. K. Rydberg constant RH = 1.O9'7x107/m.. .f Charge of electron e = 1.6 Xx 1049. Latent heat of vaporization of butane at 300°K, = 1045KJ/kg W Molecular mass of butane = 58 g. i c//*0 Molecular mass of water = 18g. Molecular mass of nitrogen = 28 g . Pressure of saturated water vapour PS -7' 2.32X103Pa at 20°C. -
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Section A: attempt all questions. (55marks)
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1. The current in a solenoid is 0.0361’-l when the solenoid is connected to an 18-kHz generator. The solenoid has a cross-sectional area of 3.1xlO-5m? and a length of2.5cm. The solenoid has 135 turns. Determine the peak voltage of the generator. (41narks) 2. Two plane mirrors are facing each other. They are parallel, 8.00cm apart, and 17.00cm long, as the figure l indicates. A laser bearn is directed at the top mirror from the left edge of the bottom of the mirror. (a) the smallest and (b) largest angle of incidence 9 that allows the beam to hit each mirror once or less?
l
31”“ m3’;£e” *1‘
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cl = 3.00crn ~
/l\ l | l l l
(Zmarks)
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L = 17.0 cm ------------ -- l
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3. Two parallel slits are illuminated by light composed of two wavelengths, one of which is 486nm. On viewing the screen, the light whose wavelength isplzndwn produces its third dark fringe at the sarne place where the light whose wavelength is unknown produces its fourth—order bright fringe. The fringes are counted relative to the central or zero—order of bright fringe. What is the length of the unknown wavelength?
7\ ..'
4. Find (a) the longest and (b) the shortest wavelengths of the Balmer series. e-
5. An X-ray tube is being operated at a potential difference of 45.0 kV.. What is the Bremstrahlung wavelength that corresponds to 25% of kinetic energy with which an electron collides with the metal target in the tube?
[3marks) [3marks)
|3marks)
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A steel bottle of volume V= 24 litres is closed at its mouth by a tap and contains a mass mg = l2Kg of liquid butane in thermodynamic equilibrium with a mass mg of butane at gas state. The volume of the liquid butane is V@= 20litres. The temperature and pressure at equilibrium are T1 =3OOK and P1= 4.5x1O5 pa respectively. Assume that the gaseous butane behaves as an ideal gas. a] Show that mg is negligible compared with mg.
(2marks}
1-‘
b) Calculate the volume V2 occupied by the mass mg when mg is entirely converted into gas under pressure P1 and temperature T1. [lmarkl c) determine the quantity of heat needed to vaporize mg at constant temperature T1.
(lmark)
A ball of mass m is dropped without initial velocity from an altitude ho above the ground. Applying the law of conservation of mechanical energy, determine the velocity V0 of the ball when
it arrives on the ground.
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(4-marks]
A rectangular flat frame 50cm by 50cm consisting of N turns p
.
->
is placed in a uniform magnetic induction B . The frame is rotating about an axis (A) situated in its plane and perpendicular to E . The angular velocity of the frame to = gis constant and at t= 0, 9 = O. .
A
C/hi f’ _
(a) Determine the expression of the induced electromotive force
5 i
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(Zmarks)
(b) Calculate the maximum amplitude of this induced emf if B= 5 x l0*5T, N = 200 turns and to = 15 revolutions
Per second.
g 3
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1 My lljnglgil
Consider two transparent media with refractive indices n1 and ng separated by a spherical surface of radius R. Light entering the spherical surface is refracted. (a) Write a relation between object distance 12, image distance
Q and radius of curvature R.
5 __=
(b) Specify the convention sign adopted for R. 1!
I
(Imark) (lmark)
(c) Calculate the object focal length fand image focal length f ' in terms of n1, nzand R.[Zmarks]
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129 - Page 3 of lll
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t/i0. The heels on a pair of a woman’s shoes have a radius of 0.5 cm at the bottom. If 30% of the weight of a woman having 60Kg is supported by each heel, find the stress on each heel. (Smarks)
1
l 1. When a steel wire stretched between two clamps is plucked, waves travel along the wire with a speed of 80m/ s. A second wire of the same material but of twice the length and twice the radius of the first is stretched between two points under the same tension as the first. At what speed will transverse Waves travel along the second wire?
(4marks)
12. (a) Find the equivalent of the group of capacitors shown in figure 2 below .
(3marks]
I
‘ j 3
4pF
I1 u
6v
2pF
l— 4pF
~.
-4pF
at/\ 4pF
(figure 2}
[b) Find the total energy stored by the group of capacitors from figure 2 above. i
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J_
13. A 50g sample of a conducting material is all that is available. The resistivity of the material is l 1x10-5Q.m, and the density is 7.86g/cm3. A wire of total resistance 1.5 Q is to be made
l
(2marks| "
out of the material. (al What is the length of the material required?
(2.5marks]
(b~)
(1.5marks]
must be the diameter of the wire? f. -»'
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14. A power transmission line consists of two parallel wires each having a cross-sectional area A. (One wire serves as a return line, so the effective length is 28 ). Show that the power lost ashheat in the conductors is given by A ' i
2
/FPloss =
2/DEPL 1 2 AV cos (D
53 L \
Zmarks)
Where cos W_o—o"oio_, (1).... :
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(b) Repeat the part (a) (ii) but using mechanical energy of the system.
(Smarks)
17. A crate of mass l0Kg is pulled up a rough incline with an initial speed of 1.5m/ s. The pulling force is lO0N parallel to the incline that makes angle of 20° with the horizontal. The coefficient of kinetic friction is 0.4 and the crate is pulled a distance of 5m. (a) How much work is done by gravitational force?
ll 1.51narks)
(b) How much work is done by the friction force ?
~[3.5Inarks)
(c) How much work is done by the IOON force?
lI1.5marks)
(d) What is the change in kinetic energy of the crate?
:;1.5marks)
,!(e) What is the speed of the crate after being pulled 5m?
(2 marks)
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M,
,4 18. Positive changes are located at three corners of a rectangle l as shown in figure 4 .F‘ind the electric field (magnitude and direction) at the fourth corner .
(lflmarks)
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0.61:1
3nC
5nC (figure 4)
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(ii) Two train whistles have identical frequencies of 1801-Iz. When one train is at rest in the station sounding its iivhistle, a beat frequency of 21-lz_ is heard from the train- What are two possible‘ speeds and directions can the moving train have? .\
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T" in!-Phat of 10
(10marks)
7"” 7 20. Over a region where the vertical component of earth's magnetic field is 40uT, a 50cm length of wire is moved with a speed of 5m/ s along U~shaped rails as shown in diagram figure 5. /V‘
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(figure5)
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the induced current in the circuit if there is a resistor qr /, 1/,L ; *:l‘E{ of 5Q in the u —shaped track. The resistance of the wire '* ,1 ,./I =;>\
I
._._.i_ ,. .._.-_.. -__- _._.;
~\f
- -_»»;.J..v..»
.
,.
»-..___,v_ wt ,v;/_- -___ _._ _ -
N .
- --an ~_- =
..-
E: rks]
Physics I
I
rks
rks
,.
\-
I
t
afl§%’é’§“Q:‘b”,.1.>:\.6);§ ‘ es Eflm¢°
8.30am -11.30am
ii
*
»xn\"'l$
129
rk) rk]
'
it I
07 Nov. 2007
-
RWANDA NATIONAL EXAMINATIONS COUNCIL
l
A
rk) rk) rk)
W
I ,
V
|
P.O.BOX 3817 KIGALI-TEL/' FAX : 586871 Y
ADVANCED LEVEL NATIONAL EXAMINATION 2007 SUBJECT
: PHYSICS I
OPTION
: MATHEMATICS-PHYSICS
TIME
21-»
: 3 HOURS
1 V
0'
z .
_
/ f/ HR~‘-___.-r _.
INSTRUCTIONS:
Thispaper consists of THREE Sections A, B and C.
.‘
Section A: Attempt ALL 15 questions. (55 marks) Section B: Attempt any THREE questions. (36 marks) Section C: Attempt ONE question only. [15 marks) Yourggay use the following information if needed. Speed oT'ligh't in a vacuum or in air c= 3x 108m/s Speed of sound in air = 345m /s. Acceleration due to gravity g =9.80m/ s2. Planckfs constant h = 6.63 X lO"34 J.S. Permittivity of free space so = 8.852110-12 C2/N.m2 - / Permeability of free space no = 41: x 10-7 Wb]A.m2 Universal constant of gases R = 8-31 F]/mol. K. Rydberg constant RH = 1.O9'7x107/m.. .f Charge of electron e = 1.6 Xx 1049. Latent heat of vaporization of butane at 300°K, = 1045KJ/kg W Molecular mass of butane = 58 g. i c//*0 Molecular mass of water = 18g. Molecular mass of nitrogen = 28 g . Pressure of saturated water vapour PS -7' 2.32X103Pa at 20°C. -
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I
\
‘
i "‘ '
J in
-
.»M€LjU\ f
1 lb: 4"?-~-N6 “'5/‘l"'€,. i
is
__.._+...____h V \
129 -Page l of 10
iJ
3-
._
at‘"
.
‘_7"3f_> !
Section A: attempt all questions. (55marks)
//A
I
I
., ;
éifi
--—
1. The current in a solenoid is 0.0361’-l when the solenoid is connected to an 18-kHz generator. The solenoid has a cross-sectional area of 3.1xlO-5m? and a length of2.5cm. The solenoid has 135 turns. Determine the peak voltage of the generator. (41narks) 2. Two plane mirrors are facing each other. They are parallel, 8.00cm apart, and 17.00cm long, as the figure l indicates. A laser bearn is directed at the top mirror from the left edge of the bottom of the mirror. (a) the smallest and (b) largest angle of incidence 9 that allows the beam to hit each mirror once or less?
l
31”“ m3’;£e” *1‘
l
“ii-
' 1aS¢1fl
l
i
cl = 3.00crn ~
/l\ l | l l l
(Zmarks)
-
I
..
L = 17.0 cm ------------ -- l
-1’I .
lfi-2111: 1) - -
3. Two parallel slits are illuminated by light composed of two wavelengths, one of which is 486nm. On viewing the screen, the light whose wavelength isplzndwn produces its third dark fringe at the sarne place where the light whose wavelength is unknown produces its fourth—order bright fringe. The fringes are counted relative to the central or zero—order of bright fringe. What is the length of the unknown wavelength?
7\ ..'
4. Find (a) the longest and (b) the shortest wavelengths of the Balmer series. e-
5. An X-ray tube is being operated at a potential difference of 45.0 kV.. What is the Bremstrahlung wavelength that corresponds to 25% of kinetic energy with which an electron collides with the metal target in the tube?
[3marks) [3marks)
|3marks)
I7
1 -M in .
' ‘ p‘
»—
...
‘
'
J
A steel bottle of volume V= 24 litres is closed at its mouth by a tap and contains a mass mg = l2Kg of liquid butane in thermodynamic equilibrium with a mass mg of butane at gas state. The volume of the liquid butane is V@= 20litres. The temperature and pressure at equilibrium are T1 =3OOK and P1= 4.5x1O5 pa respectively. Assume that the gaseous butane behaves as an ideal gas. a] Show that mg is negligible compared with mg.
(2marks}
1-‘
b) Calculate the volume V2 occupied by the mass mg when mg is entirely converted into gas under pressure P1 and temperature T1. [lmarkl c) determine the quantity of heat needed to vaporize mg at constant temperature T1.
(lmark)
A ball of mass m is dropped without initial velocity from an altitude ho above the ground. Applying the law of conservation of mechanical energy, determine the velocity V0 of the ball when
it arrives on the ground.
'
' .
~
'
(4-marks]
A rectangular flat frame 50cm by 50cm consisting of N turns p
.
->
is placed in a uniform magnetic induction B . The frame is rotating about an axis (A) situated in its plane and perpendicular to E . The angular velocity of the frame to = gis constant and at t= 0, 9 = O. .
A
C/hi f’ _
(a) Determine the expression of the induced electromotive force
5 i
»
(Zmarks)
(b) Calculate the maximum amplitude of this induced emf if B= 5 x l0*5T, N = 200 turns and to = 15 revolutions
Per second.
g 3
/J ' I
1 My lljnglgil
Consider two transparent media with refractive indices n1 and ng separated by a spherical surface of radius R. Light entering the spherical surface is refracted. (a) Write a relation between object distance 12, image distance
Q and radius of curvature R.
5 __=
(b) Specify the convention sign adopted for R. 1!
I
(Imark) (lmark)
(c) Calculate the object focal length fand image focal length f ' in terms of n1, nzand R.[Zmarks]
(W
€>é9
e
\ \_
,...-_.._._
5%)
"/i /;'k'§]Zl X/ lfiti;
w~.~"“'»-,.
. ~*
129 - Page 3 of lll
‘f Fl
'~-~
—
'
"rm
-
—
+
_|
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7
ii
1-’.I
t/i0. The heels on a pair of a woman’s shoes have a radius of 0.5 cm at the bottom. If 30% of the weight of a woman having 60Kg is supported by each heel, find the stress on each heel. (Smarks)
1
l 1. When a steel wire stretched between two clamps is plucked, waves travel along the wire with a speed of 80m/ s. A second wire of the same material but of twice the length and twice the radius of the first is stretched between two points under the same tension as the first. At what speed will transverse Waves travel along the second wire?
(4marks)
12. (a) Find the equivalent of the group of capacitors shown in figure 2 below .
(3marks]
I
‘ j 3
4pF
I1 u
6v
2pF
l— 4pF
~.
-4pF
at/\ 4pF
(figure 2}
[b) Find the total energy stored by the group of capacitors from figure 2 above. i
_.--
J_
13. A 50g sample of a conducting material is all that is available. The resistivity of the material is l 1x10-5Q.m, and the density is 7.86g/cm3. A wire of total resistance 1.5 Q is to be made
l
(2marks| "
out of the material. (al What is the length of the material required?
(2.5marks]
(b~)
(1.5marks]
must be the diameter of the wire? f. -»'
SJ '9 . I, “
.1
at
\
l \\ \“‘~-.___ _
f
m-mmwuao
_ '
/' -/ 2/ ,». .
»
Y .
k/itv/-"ii ,=
,/
%
14. A power transmission line consists of two parallel wires each having a cross-sectional area A. (One wire serves as a return line, so the effective length is 28 ). Show that the power lost ashheat in the conductors is given by A ' i
2
/FPloss =
2/DEPL 1 2 AV cos (D
53 L \
Zmarks)
Where cos W_o—o"oio_, (1).... :
L;_,C__ .-_H.
--liq-3€@c'v< 129-Page5ofl0
A
1
as
—
——
~
I
-
We
——~——
(b) Repeat the part (a) (ii) but using mechanical energy of the system.
(Smarks)
17. A crate of mass l0Kg is pulled up a rough incline with an initial speed of 1.5m/ s. The pulling force is lO0N parallel to the incline that makes angle of 20° with the horizontal. The coefficient of kinetic friction is 0.4 and the crate is pulled a distance of 5m. (a) How much work is done by gravitational force?
ll 1.51narks)
(b) How much work is done by the friction force ?
~[3.5Inarks)
(c) How much work is done by the IOON force?
lI1.5marks)
(d) What is the change in kinetic energy of the crate?
:;1.5marks)
,!(e) What is the speed of the crate after being pulled 5m?
(2 marks)
u
M,
,4 18. Positive changes are located at three corners of a rectangle l as shown in figure 4 .F‘ind the electric field (magnitude and direction) at the fourth corner .
(lflmarks)
6nC
i
' 0.2 m 1
0.61:1
3nC
5nC (figure 4)
__
(ii) Two train whistles have identical frequencies of 1801-Iz. When one train is at rest in the station sounding its iivhistle, a beat frequency of 21-lz_ is heard from the train- What are two possible‘ speeds and directions can the moving train have? .\
f\ *4 »--
ff
T" in!-Phat of 10
(10marks)
7"” 7 20. Over a region where the vertical component of earth's magnetic field is 40uT, a 50cm length of wire is moved with a speed of 5m/ s along U~shaped rails as shown in diagram figure 5. /V‘
an
,3?
§ +\s;Z°*\
.1
\
R
.
xxxxxx xxxxxx xxxxxx
T
xxxxxx xxzoéxx
L
Z
)6" 2,;/" '90 ‘Joeiéfacats
(figure5)
A' 1/
the induced current in the circuit if there is a resistor qr /, 1/,L ; *:l‘E{ of 5Q in the u —shaped track. The resistance of the wire '* ,1 ,./I =;>\
