DATA AND FORMULAE Data speed of light in free space, permeability of free space, permittivity of free space,
3.oox1o3ms1 47rx107Hm1 8.85x10-12Fm1 / (36rr)) x10'gFmr le 1.60 x 10 c
(1
elementary charge, the Planck constant, unified atomic mass constant, rest mass of electron, rest mass of proton, molar gas constant, the Avogadro con$tant, the Boltzmann constant, gravitational consiant, acceleration of free fall,
6.63x1034Js 1.66 x 10 'z7 kg 9.11 x 10 31 kg 1 .67 x 10-27 kg 8.31 JKlmol 1 6.02 x 1023 mol-1 1.38 x 10 '?3 J Kr 6.67 x 1o 11 N m2 kg-' 9.81 ms 2
Formulae uniformly accelerated motion,
ut+%a( .2
pav
work done on/by a gas, hydrostatic pressure, gravitational potential,
u2 + 2as
pgh Gm 0
displacement of particle in s.h.m., velocity of particle in s. h.m.,
xo
sin rdf
vacosal
torJU; resistors in series, resistors in parallel, electric potential, alternatinq currenvvoltage, transmission coefficient,
R
R1
x'J
+R2+
1lR1+ 1lR2+ Q / 4ntor xasin.'
T
.
t
exp(-2kd) 8n'n(LJ - E)
radioactive decay, decay constant,
xa
I
exp(-.lt)
0 693
Section A Answer all questions Six molecules are moving with the speeds and directions shown.
+--o 250 m s-r
250 m
s-1
Ct---'
Ct_+
300 m s-l
450 m
s-1
+-O
O*
450 m s'r
500 m
s'
What is the root mean square speed of these molecules?
359ms1
2
367ms1
A balloon with a volume of
4OOO cm3
400msr
381 m s1
contains helium at a pressure of 1 .20 x 105 Pa.
How many moles of helium are in the balloon if each helium atom has an average kinetic energy of 3.6O x 10'22 J?
A
3
B
1.1',|
c
1.44
D
2.22
A gas with molecular mass of M at a temperature
f
332
has a root-mean-square speed
of c/. Another gas with tvuice the molecular mass and at three times the temperature has a root-mean-square speed of c2. What is lhe .atio c1/c2?
A
E !6
c
B
D
"6
The graph below shows the variation of temperature with time for 1 kg of a substance. The substance is initially a solid, and is heated at a constant rate until all
of it vapourises. At any point, any vapour formed is allowed to escape freely out of the container. Temperature /
oC
Tr Time / min 10
12
Which of the following statements is correct?
A B
The latent heat of fusion is greater than the latent heat of vapourisation.
The amount of energy required to vapourise all of the substance at temperature 12 is approximately twice the energy required to turn the substance from a solid at 0 'C to a liquid and then to raise its temperature to Tz.
C
The specific heat capacity in the liquid state is higher than that in the solid state.
D
lf the substance is vapourised in a sealed container, it would require less energy to vapourise everything.
5
An experiment is conducted to investigate the relationship between the volume yof a fixed mass of an ideal gas and its pressure p, while keeping its temperature conslant. Which the graph shows the correct relationship at temperatures f7 and 12, where Tr > Tt?
\
c
\\
\..--_
-''--p
i:
Four charges of equal magnitude are arranged along the circumference of a circle.
li the magnitude of the electic field strength at the centre of the circle due to each charqe is E, what is the magnitude and direction of the resultant eleciric field sirength at the centre of the circle?
A
J2 E towards the left
B
\i 2 E
c
(."E -
D
("E - t)e ao*n*aras
downwards 1)
r
towaros the tett
The equipotential lines of a positive charge are drawn as shown.
12V
--. o a.
Calculate the amount of work that has to be done on an electron to move it to from point P to point Q (e is the elementary charge).
A
8e
B
-2e
C
+2e
D
+8e
The diagram shows how the electric potential energy of a charged particle varies along a straight line within an electric field. Electric potential energy
Distance
At which point is the magnitude of electric force acting on the charged particle a minimum?
BBCCDD The force of attraction between 2 unlike charges is 2.0 N. lf the distance between
them is increased to 3 times the original value, what is the force of attraction between them?
A
0.22 N
B
0.33 N
c
0.44 N
D
0.66 N
10
Two conducting metal plates are placed parallel to one another as shown in the diagram. The potential ofone plate is +yand the other is +5y. +V
+5V The space bet\rveen the plates is divided equally by the dotted lines. P and Q are 2 points that lie on the lines as shown- Determine the expression for the amount of work required to move a unit posiiive charge from pojnt P to point Q.
a4v 11
B
-2V
c
+2V
D
+4V
A wire P with resistivity, p, and length, /, has a resistance R. lf the wire is stretched
and its length is increased by 5% what would be the change in resistance of the wire? (Assume the volume of the wire has not changed.)
A
12
104/.
B
-
5v"
5%
D
100/0
The diagram shows a circuit consisting of a cell, E, and a variable resistor, R.
lf the electromotive force of the cell is 10.0 V and the internal resistance of the cell is 2.00 O calculate the maximum power that is delivered to R.
5.00
w
125W
250W
50.0
w
13
When 15.0 C of charge flows through a pariicular resistor 5.0 J of energy are converted. What is the potential difference across the resistor?
30v
0.33 V
14
20v
75V
An electrical kettle requires 0.10 kwh of energy to bring its contents to a
boil.
Express this amount of energy in terms ofjoules.
0.028 J
15
6x1o3J
0.36 J
3.6 x 105 J
The diagram below shows connected wires which carry cuffents of various values. What is the value and direction of the current / in shown in the diaoram?
16
A
I
A away from X
B
1
c
11 A away from X
D
ll
A towards X
AtowardsX
ln the potentiometer above, a balance length of 0.70 m is obtained. The length of the resistance wire XY is 1.0 m. 10 0
v
What is the resistance of XY?
A
6.0 0
B
6.3 0
c
8.3
c)
D
10 ()
17
An e.m.f. source E of internal resistance r, is connected to an external resistor of resistance R. Which of the following graphs represents how the current, 1, through the external resistor, varies with the potential difference, y, across the resistor R?
'18
The circuit below consists of 10 identical resistors of resistance R.
What is the effective resistance across X and Y?
2R
c17
6
3R
19
The graph above shows how the resistance Rr of the thermistor varies with temperature f. Rr/Q BO
60 4.0 2.0
What is the potential difference 20 "c?
A 20
1.2
B
V
y
2.4V
across the 8.0 O fixed resistor, when
C
3.6V
D
I
is
4.BV
A cuffent passing through a solenoid sets up a magnetic field around it. Which of the following will result in a stronger magnetic field strength within the solenoid?
I ll lll
increasing the current through the solenoid using a shorter solenoid
inseriing a soft iron core into the solenoid
A
land ll only
B
land lll only
c
ll and lll only
D
I, ll and lll
A loop of flexible wire lies in a loose, irregular shape on the surface of a smooth horizontal table. A uniform steady magnetic field of flux density I is directed vertrcally downwards tl^'ough the table.
to batiery
B into surface of table lf the ends of the wire are connected to a battery such that there is a current in the loop in the direction shown, which oi the following is likely to be observed?
A B c D 22
The loop of wire moves vertically above the surface of the table The loop ofwire moves horizontaliy on the surface of the table The loop ofwire expands into a circle. The loop ofwire collapses.
A length of cuffent-carrying wire PQRST is placed in a region of uniform magnetic field as shown in the diagram.
B field
Determine which segment of the wire experiences the greatest magnetic force
APO
QR
CRS
ST
23
A 2 kg mass is attached to a 5 kg mass by a light inextensible strino which runs through a smooth pulley.
smooth oullev
lf the slope on which the 2 kg mass lies is frictionless, determine the acceleration of the 2 masses.
B
24
1.40 m
981 ms2
5.61 m s2
s-2
When a force, F, varying as shown below, is applied to a mass of 10 kg, the gain in momentum in 5 s is 40 kg m
s-1.
F/N
time / s What is the value of x?
A
25
c
B
'10
D
15
Two stars of equal mass M move with constant speed v in a circular orbit of radius R about their common centre of mass as shown in the diagram below.
Which of the following is th e correct expresston tot v1
A
Fn
!zn
IGM
D
Section B Answer all questions A fixed mass of monatomic ideal gas is made to undergo the processes shown in the table below. The initial state of the gas is denoted by A where the gas has 4.0 x 105 Pa, volume of 7.5 x
'10 3 m3
a pressure of
and a temperature of 450 K. 'l O 3
AtoB
Gas is allowed
BtoC
Gas is cooled at constant pressure to a temperature of 300 K.
CtoD
Gas is compressed isothermally lo a pressure of 4.0 x 105 Pa.
DtoA
Gas is allowed to expand at constanl pressure until it returns to its initial state at A.
10
expand isothermally until its volume is 10.0 x
m3.
plPa 40x'105-
Vc
(axi)
7.5 x 10-3 10.0 x 103
Explain what is meanl by internal energy
.....111
(ii)
For an ideal gas, explain why internal energy is dependent on its thermodynamic temperature only.
I1l
(bxi)
Calculate the number of moles of ideal gas in the sample.
number of moles =
(ii) Using the ideal gas equation, or otherwise,
I1l
determine pc and yc, the pressure and volume
respectively for the gas at C.
Pa
mt [3]
(iii)
Calculate the work done on the gas during the process B to C.
work done on gas =
J l2l
(iv)
By considerinq the change in temperature, calculate the change in infernal energy of the gas as it goes from siate B to siate C.
change in internalenergy
(v)
J I2I
=
Hence, detennine the amount of heat which the gas exchanges wilh its surroundings during
lhe process from B to C. State clearly if heat flows into or out of the gas.
amount of heat exchanged
=
direction of heat flow =
(c)
.................-.........
J
.............................. I2l
For the overall cyclic process ABCDA, state if the net heat flow is into or out of the gas. Without making detailed calculations, explain your answer.
2
(al
+40
v
20v
(D
V
11]
J
12]
v m'
[3]
(ii)
loss in linelic energy = (;iD
Determine the approxrmate value of the eleclric field strength ai C.
electric field strenqth =
(iv)
Sketch, on Fig.2.2, the variation ofthe eleckic potenlialalong AB. Eleclric potential
I2l
Dislance
(b) An electron is released from rest at the position shown in Fig. 2.3. Two stationary protons are in the vicinity ofthe electron.
Fig.2.3
(i)
Describe the subsequent motion ofthe electron.
t2l
(ii)
Determine the maximum kinetic energy which the electron attains during ils motion. Leave your answer in terms of e and r, where e is lhe elementary charge.
maximum kinetic energy= ..............................t31
{iii)
At the position where the electron has maximum KE, sketch the eleclric field pattern due to the interaction of the 3
charges.
121
3
(a) Define the volf and use energy considerations to distinguish bet\reen electromotive force ot a cell and potential differerce behreen its terminals.
t3l
(b)
A battery of e.m.f. 12.0 V and intemal resistance 0.50 O is connected to a resistor of resistance 7.50 Q as shown in Fig 3.'1.
= 12.O V
R=7.50O
= 0.50 c)
B
Fig 3.1
(i)
Mark with an X, on Fig 3.1, the position of a switch so that the voltmeter may be used
to measure either the e.m.f. Eof thecell ortheterminal potential difference
V.
ill
Determine
(ii)
the cuffent in the circuit,
cUrrent =
A [2]
(iii)
the potential difierence across the 7.50 O resistor,
potenlial difference =
(iv)
(v)
(c)
V
12]
potential at A =
V
111
potential at B =
v
[1]
power =
.............................. w
I21
the potential at poinls A and B in the circuit,
the power supplied to the 7.50 O resistor.
Explain why the potential difference across the terminals of the cell is normally lower than
the cell's e.m.f. Under what condition is the potential difference across a cell's terminals equalto its e.m.f.?
4(a)
Fig. 4.1 shows a circuit containing a 10.0 V battery with a non negligible internal resistance r, and 6 external resistors.
Fig.4.1 The potential differences across some ofthe resistors are given in Table 4.1 below. Potential Difference / V
B
4A
c
3.0
D
10 Table 4.1
lesislor.
(D
Conp ete -able 4.1 lo show ll.e polen|al difference across each
(i0
Write down the values of the electric potential at positions V and Y.
I3l
polential at V =
v
t1l
potential at Y =
V
11]
(b) The potentiometer in Fiq. 4.2 consists of a non-ideal driver cell of e.m.f. 12.0 V with internal resistance of 2.5 O, a standard cell of e.m.f. E, and a 1-metre resistance wire XY. The total resistance of XY is 8.0 O. Switch B is connected to part of lhe resistance wire at points K and Y usinq connecting wires, such that length l(Y along the resistance wire is 20.0 cm.
200cm
Swilch A
Fig.4.2 (i)
When Switch A is closed, and Switch B is opened, the balanced length is 60.0 cm,
'1.
What is the potential difference belween length XJ?
potential difference =
V
12]
V
13]
Calculate the e.m.f. E of the slandard cell.
(ii)
When Swiich B is closed, and Switch A is opened, calculate the new balanced lenqth.
balanced length
(iii)
=.............................. m
[3]
With both Switch A and B both opened, state and explain one factor which can increase the balanced length XJ.
t11
5
(a) A narrow beam of coherent light of wavelength 589 nm is normally incident on a diffraction grating with 5.00
(i)
x
105
lines per melre.
Find the total number of bright fringes that are visible on a screen placed at distance
number of bright fringes =
(ii)
......................... . m [3]
Stale 2 ways 10 increase the number of brighl fringes observed on the screen.
...121
(b) Fig. 5.1 consists of a conducting rod XY which is placed on 2 horizontal parallel aluminium rails AB and CD. The mass of rod XY is 12.0 g.
Fiq.5.1 A uniform magnetic field of strength 0.200 T acts perpendicularly to the plane of the page, such thal when lhe switch is closed, rod XY moves to lhe left.
(i)
State the direction of the current flow within rod XY when the switch is closed. direciion of current =
Ill
(ii)
State the direction ofthe uniform magnetic field-
ofmagneticfield=
direction
(iii)
...
.
.. [1]
When the switch is closed, a current of 2.50 A flows in the circuit. Calculate the magnetic force acting on rod XY if it has length 8.00 cm.
magnetic force =
(iv)
N
12]
To stop rod XY from moving to the left, the aluminium rails can be lilted. At this equilibrium position where rod XY is stationary, draw lhe free bodv diaqram of rod XY, indicating allthe forces acting on it. (Hint: draw the cross-section of rod XY.)
(v)
I2l
Determine the angle to the horizontal which the aluminium rods must be tilted lo keep rod XY stationary.
angle to horizontal =
............................." t4l
