35

AS General Physics questions

1.When a voltage V of 12.2 V is applied to a DC motor, the current I in the motor is 0.20 A. Which one of the following is the output power VI of the motor given to the correct appropriate number of significant digits?

A.2 WB.2.4 W

C.2.40 WD.2.44 W

(1)

2.The diagram below shows a boat that is about to cross a river in a direction perpendicular to the bank at a speed of 0.8 m s1. The current flows at 0.6 m s1 in the direction shown.

0.8 ms

Boat

Bank

Bank

1

1

0.6 ms

The magnitude of the displacement of the boat 5 seconds after leaving the bank is

A.3 m.B.4 m.

C.5 m.D.7 m.

(1)

3.Which one of the following units is a unit of energy?

A.eVB.W s1

C.W m1D.N m s1

(1)

4.Natalie measures the mass and speed of a glider. The percentage uncertainty in her measurement of the mass is 3% and in the measurement of the speed is 10%. Her calculated value of the kinetic energy of the glider will have an uncertainty of

A.30%.B.23%.

C.13%.D.10%.

(1)

5.The ratio

atom

an

of

diameter

nucleus

a

of

diameter

is approximately equal to

A.1015.B.108.

C.105.D.102.

(1)

6.Which one of the following lists a fundamental unit and a derived unit?

A.

ampere

second

B.

coulomb

kilogram

C.

coulomb

newton

D.

metre

kilogram

(1)

7.A student measures the current in a resistor as 677 mA for a potential difference of 3.6 V. A calculator shows the resistance of the resistor to be 5.3175775 . Which one of the following gives the resistance to an appropriate number of significant figures?

A.5.3 B.5.32

C.5.318 D.5.31765775

(1)

8.Two forces of magnitudes 7 N and 5 N act at a point. Which one of the following is not a possible value for the magnitude of the resultant force?

A.1 NB.3 N

C.5 ND.7 N

(1)

9.A student measures a distance several times. The readings lie between 49.8 cm and 50.2 cm. This measurement is best recorded as

A.49.8 0.2 cm.B.49.8 0.4 cm.

C.50.0 0.2 cm.D.50.0 0.4 cm.

(1)

10.The diameter of the nucleus of a hydrogen atom is of the order of

A.108 m.B.1015 m.

C.1023 m.D.1030 m.

(1)

11.The unit, the electron-volt is equivalent to

A.1.6 1019 J.B.1.0 J.

C.1.6 1019 J.D.9.1 1031 J.

(1)

12.The time period T of oscillation of a mass m suspended from a vertical spring is given by the expression

T = 2

k

m

where k is a constant.

Which one of the following plots will give rise to a straight-line graph?

A.T2 against mB.

T

against

m

C.T against mD.

T

against m

(1)

13.Which one of the following is a vector quantity?

A.Electric powerB.Electrical resistance

C.Electric field strengthD.Electric potential difference

(1)

14.The power dissipated in a resistor of resistance R carrying a current I is equal to I2R. The value of I has an uncertainty of 2% and the value of R has an uncertainty of 10%. The value of the uncertainty in the calculated power dissipation is

A.8%.B.12%.

C.14%.D.20%.

(1)

15.The number of heartbeats of a person at rest in one hour, to the nearest order of magnitude is

A.101.B.102.

C.103.D.105.

(1)

16.The diameter of a proton is of the order of magnitude of

A.1012 m.B.1015 m.

C.1018 m.D.1021 m.

(1)

17.An ammeter has a zero offset error. This fault will affect

A.neither the precision nor the accuracy of the readings.

B.only the precision of the readings.

C.only the accuracy of the readings.

D.both the precision and the accuracy of the readings.

(1)

18.Which one of the following is a scalar quantity?

A.PressureB.Impulse

C.Magnetic field strengthD.Weight

(1)

19.Which one of the following is a fundamental unit?

A.CoulombB.Ohm

C.VoltD.Ampere

(1)

20.When a force F of (10.0 0.2) N is applied to a mass m of (2.0 0.1) kg, the percentage uncertainty attached to the value of the calculated acceleration

m

F

is

A.2%.B.5%.

C.7%.D.10%.

(1)

21.Which one of the following is a fundamental unit?

A.CoulombB.Ohm

C.VoltD.Ampere

(1)

22.Which of the following gives the approximate ratio of the separation of the molecules in water and in steam at atmospheric pressure?

Water :

Steam

A.

1 :

1

B.

1 :

10

C.

1 :

100

D.

1 :

1000

(1)

23.The resistive force F acting on a sphere of radius r moving at speed v through a liquid is given by

F = cvr

where c is a constant. Which of the following is a correct unit for c?

A.NB.N s1

C.N m2 s1D.N m2 s

(1)

24.Which of the following is the best estimate, to one significant digit, of the quantity shown below?

(

)

9

.

15

1

.

8

A.1.5B.2.0

C.5.8D.6.0

(1)

25.Two objects X and Y are moving away from the point P. The diagram below shows the velocity vectors of the two objects.

P

Velocity vector for object Y

Velocity vector for object X

Which of the following velocity vectors best represents the velocity of object X relative to object Y?

A.

B.

C.

D.

(1)

26.A student measures two lengths as follows:

T = 10.0 0.1 cmS = 20.0 0.1 cm.

The student calculates:

FT, the fractional uncertainty in TFS, the fractional uncertainty in SFTS, the fractional uncertainty in (T S)FT+S, the fractional uncertainty in (T + S).

Which of these uncertainties has the largest magnitude?

A.FTB.FS

C.FTSD.FT+S

(1)

27.A student moves between two points P and Q as shown below.

point P

y

direction

point Q

x

direction

The displacement from P in the x-direction is dX. The displacement from P in the y-direction is dY. The resultant displacement from P is dR.

Which of the following diagrams shows the three displacements from point P?

A.

C.

B.

D.

P

P

P

P

Q

Q

Q

Q

d

X

d

X

d

X

d

X

d

Y

d

Y

d

Y

d

Y

d

R

d

R

d

R

d

R

(1)

28.The order of magnitude of the weight of an apple is

A.104 N.B.102 N.

C.1 N.D.102 N.

(1)

29.Which one of the following contains three fundamental units?

A.

Metre

Kilogram

Coulomb

B.

Second

Ampere

Newton

C.

Kilogram

Ampere

Kelvin

D.

Kelvin

Coulomb

Second

(1)

30.The reading of a constant potential difference is made four times by a student. The readings are

1.176 V1.178 V1.177 V1.176 V

The student averages these readings but does not take into account the zero error on the voltmeter. The average measurement of the potential difference is

A.precise and accurate.B.precise but not accurate.

C.accurate but not precise.D.not accurate and not precise.

(1)

31.The variation with time t of the speed v of an object is given by the expression

v = u + at

where u and a are constants.

A graph of the variation with time t of speed v is plotted. Which one of the following correctly shows how the constants may be determined from this graph?

A.

v

0

u

0

t

gradient =

a

B.

v

0

u

0

t

gradient =

1

a

C.

v

0

0

u

t

gradient =

a

D.

v

0

0

u

t

gradient =

1

a

(1)

32.An object of mass m is hung from a spring. When the object is pulled downwards and then released, the frequency f of oscillation of the object is given by the expression

k

m

f

2

1

=

where k is a constant.

Which one of the following graphs would produce a straight-line for the variation with mass m of frequency f?

x-axis

y-axis

A.

m

f

B.

m

f

1

C.

2

1

m

f

1

D.

m

f2

(1)

33.The volume V of a cylinder of height h and radius r is given by the expression

V = r2h.

In a particular experiment, r is to be determined from measurements of V and h. The uncertainties in V and in h are as shown below.

V

7%

h

3%

The approximate uncertainty in r is

A.10%.B.5%.

C.4%.D.2%.

(1)

34.The ratio

nucleus

hydrogen

of

diameter

atom

hydrogen

of

diameter

to the nearest order of magnitude is

A.102.B.105.

C.1010.D.1015.

(1)

35.The kWh is equal to

A.1.0 103 J.B.3.6 103 J.

C.6.0 104 J.D.3.6 106 J.

(1)

36.The diagram below shows the position of the meniscus of the mercury in a mercury-in-glass thermometer.

T / C

2

4

6

8

10

Which of the following best expresses the indicated temperature with its uncertainty?

A.(6.0 0.5)CB.(6.1 0.1)C

C.(6.2 0.2)CD.(6.2 0.5)C

(1)

37.Which of the following represents two vector quantities?

A.distance, accelerationB.kinetic energy, work

C.force, momentumD.electric field strength, electric potential

(1)

38.The radius of a loop is measured to be (10.0 0.5) cm. Which of the following is the best estimate of the uncertainty in the calculated area of the loop?

A.0.25%B.5%

C.10%D.25%

(1)

39.The mass of an atom of the isotope strontium-92 (92Sr) is of the order of

A.1023 kg.B.1025 kg.

C.1027 kg.D.1029 kg.

(1)

40.Which one of the following is a fundamental unit in the SI system?

A.AmpereB.Volt

C.OhmD.Tesla

(1)

41.Which one of the following measurements is stated correctly to two significant digits?

A.0.006 mB.0.06 m

C.600 mD.620 m

(1)

42.The frequency f of an oscillating system is given by

l

g

f

p

=

2

1

where g and p are constants.

The frequency f is measured for different values of l and a graph is plotted.

Which one of the following will produce a straight-line graph?

x-axis

y-axis

A.

f

l

B.

f

l

C.

f2

l

1

D.

f2

l

(1)

43.The mass of an atom of the isotope strontium-92 (92Sr) is of the order of

A.1023 kg.B.1025 kg.

C.1027 kg.D.1029 kg.

(1)

44.The relationship between two measured quantities P and Q is of the form

P = kQn

where k and n are constants.

A plot of lg P (y-axis) against lg Q (x-axis) will enable the value of k to be determined by measuring only

A.the intercept on the lg P axis.B.the intercept on the lg Q axis.

C.the slope of the graph.D.the reciprocal of the slope of the graph.

(1)

45.An object has an acceleration of 2.0 m s2. Which of the following gives the change in the speed of the object after 7.00 s to the correct number of significant digits?

A.14 m s1B.14.0 m s1

C.14.00 m s1D.14.000 m s1

(1)

46.A particle is moving in a circular path of radius r. The time taken for one complete revolution is T. The acceleration a of the particle is given by the expression

a =

.

4

2

2

T

r

p

Which of the following graphs would produce a straight-line?

A.a against TB.a against T2

C.a against

T

1

D.a against

2

1

T

(1)

47.The diagram below shows two vectors, x and y.

x

y

Which of the vectors below best represents the vector c that would satisfy the relationc=x + y?

A.

B.

C.

D.

(1)

48.An object falls from rest with an acceleration g. The variation with time t of the displacement s of the object is given by

.

2

1

2

gt

s

=

The uncertainty in the value of the time is 6% and the uncertainty in the value of g is 4%. The best estimate for the uncertainty of the position of the object is

A.5%.B.8%.

C.10%.D.16%.

(1)

49.The mass of an electron is 9.1 1031 kg and that of a proton is 1.7 1027 kg. Which one of the following is the difference in the order of magnitude of the masses of the electron and the proton?

A.10.8B.7.4

C.5.4D.3

(1)

50.Sub-multiples of units may be expressed using a prefix. Which one of the following lists the prefixes in decreasing order of magnitude?

A.

centi-

micro-

milli-

nano-

B.

milli-

centi-

nano-

micro-

C.

centi-

milli-

micro-

nano-

D.

milli-

micro-

centi-

nano-

(1)

51.Values of current I in an electrical component and of the corresponding potential difference V across the component are plotted on a graph. Error bars for each point have been included. Which one of the following shows the best-fit line for the plotted points?

A.

I

B.

I

V

V

C.

I

D.

I

V

V

(1)

52.Which one of the following includes three vector quantities?

A.

velocity

weight

field strength

B.

weight

mass

field strength

C.

velocity

energy

weight

D.

mass

energy

field strength

(1)

53.The length of a rod is measured using part of a metre rule that is graduated in millimetres, as shown below.

10

9

8

7

6

5

4

3

2

cm

Which one of the following is the measurement, with its uncertainty, of the length of the rod?

A.5 0.1 cmB.5 0.2 cm

C.5.0 0.1 cmD.5.0 0.2 cm

(1)

54.The graph below shows the variation with ln P of a quantity x. (ln P is the natural logarithm of the quantity P.) The magnitude of the gradient of the line is g.

0

0

x

1n

P

1n

P

0

Which one of the following is the correct expression for the variation of P with x?

A.P = P0 egxB.P = P0 e+gx

C.P = P0 + egxD.P = P0 e+gx

(1)

55.The graph below shows how a quantity y varies with time t for a falling object.

y

0

0

t

Which one of the following quantities could be represented by y?

A.Speed when air resistance is negligible

B.Speed when air resistance is not negligible

C.Distance moved from rest when air resistance is negligible

D.Distance moved from rest when air resistance is not negligible

(1)

56.Which one of the following quantities is a vector?

A.WorkB.Temperature

C.Electric fieldD.Pressure

(1)

57.The volume of the Earth is approximately 1012 km3 and the volume of a grain of sand is approximately 1 mm3. The order of magnitude of the number of grains of sand that can fit in the volume of the Earth is

A.1012.B.1018.

C.1024.D.1030.

(1)

58.The period T of oscillation of a mass m attached to the end of a spring is given by

,

2

k

m

T

p

=

where k is an accurately known constant. The mass is measured as 0.500 0.045 kg.

What is the percentage uncertainty in the calculated value of the period?

A.3.0%B.4.5%

C.9.0%D.18%

(1)

59.The time interval between human heartbeats is of the order of

A.102 s.B.101 s.

C.100 s.D.101 s.

(1)

60.The kilowatt-hour is equivalent to approximately

A.60 J.B.3.6 103 J.

C.8.6 104 J.D.3.6 106 J.

(1)

61.The speed of sound v in a gas is related to the pressure P of the gas by the expression

kP

v

=

where k is a constant.

Which variables should be plotted in order to produce a straight-line graph with the slope equal to k?

A.v2 against P2B.v2 against P

C.v against PD.v against

P

(1)

62.The sides of a cube are each of length 1.00 m. Each side is measured with an uncertainty of 2%. The absolute uncertainty in the volume of the cube is

A.0.02 m3.B.0.06 m3.

C.0.2 m3.D.0.6 m3.

(1)

63.The length of a page of the examination paper is approximately 30 cm.

Which of the following gives the order of magnitude for the time taken for light to travel the length of the page?

A.107 sB.108 s

C.109 sD.1010 s

(1)

64.The variation with speed v of the force F acting on an object is given by the expression

F = pv2 + qv,

where p and q are constants.

What quantity should be plotted on the y-axis of a graph and what should be plotted on the x-axis in order to give a straight-line graph?

y-axis

x-axis

A.

v

F

v

B.

v

F

v2

C.

F

v

D.

F

v2

(1)

65.Quantity x varies with quantity y according to the expression

y = pxn,

where p and n are constants.

Values of lg x (log10 x) are plotted against the corresponding values of lg y as shown below.

1g

y

I

0

0

1g

x

The intercept on the lg y-axis is I. Which of the following gives the value of lg p?

A. IB.+ I

C. lg ID.+ lg I

(1)

66.Which of the following contains only fundamental SI units?

A.

ampere

newton

second

B.

volt

second

kelvin

C.

mole

ampere

kilogram

D.

kilogram

metre

tesla

(1)

67.The mass of a body is measured to be 0.600 kg and its acceleration to be 3 m s2. The net force on the body, expressed to the correct number of significant figures is

A.1.8 N.B.1.80 N.

C.2 N.D.2.0 N.

(1)

68.The molar mass of water is 18 g. The approximate number of water molecules in a glass of water is

A.1022.B.1025.

C.1028.D.1031.

(1)

69.Both random and systematic errors are present in the measurement of a particular quantity. What changes, if any, would repeated measurements of this quantity have on the random and systematic errors?

Random

Systematic

A.

reduced

reduced

B.

reduced

unchanged

C.

unchanged

reduced

D.

unchanged

unchanged

(1)

70.The mass of a body is measured with an uncertainty of 2.0% and its volume with an uncertainty of 10%. What is the uncertainty in the density of the body?

A.0.2%B.5.0%

C.12%D.20%

71.Which list gives the masses of the particles in ascending order of magnitude?

least greatest

A.

-particle

-particle

proton

B.

proton

-particle

-particle

C.

proton

-particle

-particle

D.

-particle

proton

-particle

(1)

72.The kilowatt-hour (kW h) is equivalent to

A.6.0104 J.B.6.0104W.

C.3.6106 J.D.3.6106W.

(1)

73.Which of the following contains three scalar quantities?

A.

mass

charge

speed

B.

density

weight

mass

C.

speed

weight

charge

D.

charge

weight

density

(1)

74.A student uses a metre rule and a set-square to measure a series of vertical heights, as shown.

set-square

metre rule

height to

be measured

The metre rule is not vertical.What type of error is reduced by using a set-square and what type of error is caused because the metre rule is not vertical?

error reduced by use ofset-square

error caused bynon-vertical ruler

A.

random

random

B.

random

systematic

C.

systematic

random

D.

systematic

systematic

(1)

75.The electrical resistance R of a component varies with temperature T according to the expression

R = R0ek/T

where R0 and k are constants.

A graph of the variation with

T

1

of lnR is drawn and a straight line is obtained. The intercept on the

T

1

axis is equal to

A.lnR0B.

k

R

0

ln

-

C.lnR0D.

k

R

0

ln

(1)

76.An elephant has a life expectancy of 60 years. Which of the following gives the order of magnitude of this lifetime?

A.1011sB.109s

C.107sD.105s

(1)

77.The frequency f of waves of wavelength travelling on the surface of deep water is given by

f =

pl

2

g

where g is the acceleration of free fall.

Which of the following will yield a straight-line graph?

y-axis

x-axis

A.

f 2

l

1

B.

f 2

l

C.

f

l

D.

f

l

1

(1)

78.The diagram below shows two vectors X and Y.

X

Y

Which of the following best represents the vector Z = X Y.

A.

Z

B.

Z

C.

Z

D.

Z

(1)

79.The period T of oscillation of a mass m on a spring, having spring constant k is T =

k

m

2

.

The uncertainty in k is 11% and the uncertainty in m is 5%. The approximate uncertainty in T is

A.4%.B.6%.

C.8%.D.16%.

(1)

80.The order of magnitude of the weight of an apple is

A.104 N.B.102 N.

C.1 N.D.102 N.

(1)

81.The density of a metal cube is given by the expression

V

M

=

where M is the mass and V is the volume of the cube. The percentage uncertainties in M and V are as shown below.

M

12%

V

4.0%

The percentage uncertainty in the calculated value of the density is

A.3.0%.B.8.0%.

C.16%.D.48%.

(1)

82.The volume V of a cylinder of height h and radius r is given by the expression

V = pr2h.

In a particular experiment, r is to be determined from measurements of V and h. The uncertainties in V and in h are as shown below.

V

7%

h

3%

The approximate uncertainty in r is

A.10%.B.5%.

C.4%.D.2%.

(1)

83.This question is about units and momentum.

(a)Distinguish between fundamental units and derived units.

.....................................................................................................................................

.....................................................................................................................................

(1)

(b)The rate of change of momentum R of an object moving at speed v in a stationary fluid of constant density is given by the expression

R = kv2

where k is a constant.

(i)State the derived units of speed v.

...........................................................................................................................

(1)

(ii)Determine the derived units of R.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

(2)

(iii)Use the expression and your answers in (b)(i) and (b)(ii) to determine the derived units of k.

...........................................................................................................................

...........................................................................................................................

(1)

(c)Define

(i)linear momentum.

...........................................................................................................................

...........................................................................................................................

(1)

(ii)impulse.

...........................................................................................................................

...........................................................................................................................

(1)

(d)In a ride in a pleasure park, a carriage of mass 450 kg is travelling horizontally at a speed of 18 m s1. It passes through a shallow tank containing stationary water. The tank is of length 9.3 m. The carriage leaves the tank at a speed of 13 m s1.

18 m s

carriage, mass 450 kg

9.3m

water-tank

13 m s

1

1

As the carriage passes through the tank, the carriage loses momentum and causes some water to be pushed forwards with a speed of 19 m s1 in the direction of motion of the carriage.

(i)For the carriage passing through the water-tank, deduce that the magnitude of its total change in momentum is 2250N s.

...........................................................................................................................

...........................................................................................................................

(1)

(ii)Use the answer in (d)(i) to deduce that the mass of water moved in the direction of motion of the carriage is approximately 120 kg.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

(2)

(iii)Calculate the mean value of the magnitude of the acceleration of the carriage in the water.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

(3)

(e)For the carriage in (d) passing through the water-tank, determine

(i)its total loss in kinetic energy.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

(3)

(ii)the gain in kinetic energy of the water that is moved in the direction of motion of the carriage.

...........................................................................................................................

...........................................................................................................................

(1)

(f)By reference to the principles of conservation of momentum and of energy, explain your answers in (e).

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

(3)

(Total 20 marks)

84.As part of a road-safety campaign, the braking distances of a car were measured.

A driver in a particular car was instructed to travel along a straight road at a constant speed v. A signal was given to the driver to stop and he applied the brakes to bring the car to rest in as short a distance as possible. The total distance D travelled by the car after the signal was given was measured for corresponding values of v. A sketch-graph of the results is shown below.

0

0

v

D

(a)State why the sketch graph suggests that D and v are not related by an expression of the form

D = mv + c,

where m and c are constants.

...................................................................................................................................

...................................................................................................................................

(1)

(b)It is suggested that D and v may be related by an expression of the form

D = av + bv2,

where a and b are constants.

In order to test this suggestion, the data shown below are used. The uncertainties in the measurements of D and v are not shown.

v / m s1

D / m

.

.

.

.

.

.

.

.

/

v

D

10.0

14.0

1.40

13.5

22.7

1.68

18.0

36.9

2.05

22.5

52.9

27.0

74.0

2.74

31.5

97.7

3.10

(i)In the table above, state the unit of

.

v

D

(1)

(ii)Calculate the magnitude of

,

v

D

to an appropriate number of significant digits, for v = 22.5 m s1.

.........................................................................................................................

.........................................................................................................................

(1)

(c)Data from the table are used to plot a graph of

v

D

(y-axis) against v (x-axis). Some of the data points are shown plotted below.

3.50

3.00

2.50

2.00

1.50

1.00

0.50

0.00

35.00

30.00

25.00

20.00

15.00

10.00

5.00

0.00

v

/ m s

1

D

v

(

S

.

I

.

u

n

i

t

s

)

On the graph above,

(i)plot the data points for speeds corresponding to 22.5 m s1 and to 31.5 m s1.

(2)

(ii)draw the best-fit line for all the data points.

(1)

(d)Use your graph in (c) to determine

(i)the total stopping distance D for a speed of 35 m s1.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

(2)

(ii)the intercept on the

v

D

axis.

.........................................................................................................................

(1)

(iii)the gradient of the best-fit line.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

(2)

(e)Using your answers to (d)(ii) and (d)(iii), deduce the equation for D in terms of v.

D = .........................................................................................................................

(1)

(f)The uncertainty in the measurement of the distance D is 0.3 m and the uncertainty in the measurement of the speed v is 0.5 m s1.

(i)For the date point corresponding to v = 27.0 m s1, calculate the absolute uncertainty in the value of

.

v

D

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

(2)

(ii)Each of the data points in (b) was obtained by taking the average of several values of D for each value of v. Suggest what effect, if any, the taking of averages will have on the uncertainties in the data points.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

(2)

(Total 16 marks)

85.The resistive force F that acts on an object moving at speed v in a stationary fluid of constant density is given by the expression

F = kv2

where k is a constant.

(a)State the derived units of

(i)force F.

...........................................................................................................................

(1)

(ii)speed v.

...........................................................................................................................

(1)

(b)Use your answers in (a) to determine the derived units of k.

.....................................................................................................................................

.....................................................................................................................................

(1)

(Total 3 marks)

86.This question is about thermal energy transfer through a rod.

A student designed an experiment to investigate the variation of temperature along a copper rod when each end is kept at a different temperature. In the experiment, one end of the rod is placed in a container of boiling water at 100C and the other end is placed in contact with a block of ice at 0.0C as shown in the diagram.

boiling water

100

C

ice

0C

temperature sensors

copper rod

not to scale

Temperature sensors are placed at 10 cm intervals along the rod. The final steady state temperature q of each sensor is recorded, together with the corresponding distance x of each sensor from the hot end of the rod.

The data points are shown plotted on the axes below.

110

100

90

80

70

60

50

40

30

20

10

0

90

80

70

60

50

40

30

20

10

0

x

/ cm

/

C

The uncertainty in the measurement of q is 2C. The uncertainty in the measurement of x is negligible.

(a)On the graph above, draw the uncertainty in the data points for x = 10 cm, x = 40 cm and x = 70 cm.

(2)

(b)On the graph above, draw the line of best-fit for the data.

(1)

(c)Explain, by reference to the uncertainties you have indicated, the shape of the line you have drawn.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

(2)

(d)(i)Use your graph to estimate the temperature of the rod at x =55 cm.

.........................................................................................................................

(1)

(ii)Determine the magnitude of the gradient of the line (the temperature gradient) atx = 50 cm.

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

.........................................................................................................................

(3)

(e)The rate of transfer of thermal energy R through the cross-sectional area of the rod is proportional to the temperature gradient

x

D

D

along the rod. At x = 10 cm, R = 43 W and the magnitude of the temperature gradient is

x

D

D

= 1.81C cm1. At x = 50 cm the value of R is 25 W.

Use these data and your answer to d(ii) to suggest whether the rate R of thermal energy transfer is in fact proportional to the temperature gradient.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

(3)

(f)It is suggested that the variation with x of the temperature q is of the form

kx

e

-

=

0

where q0 and k are constants.

State how the value of k may be determined from a suitable graph.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

(2)

(Total 14 marks)

87.This question is about the rise of water in a capillary tube.

A capillary tube is a tube that is open at both ends and has a very narrow bore. A capillary tube is supported vertically with one end immersed in water. Water rises up the tube due to a phenomenon called capillary action. The water in the bore of the tube forms a column of height h as shown below.

narrow bore

glass wall

glass wall

h

water

(a)The height h, for a particular capillary tube was measured for different temperatures of the water. The variation with temperature q of the height h is shown below. Uncertainties in the measurements are not shown.

17

16

15

14

13

12

11

10

9.0

8.0

90

80

70

60

50

40

30

20

10

0

h

/ cm

/

C

(i)On the graph above, draw a best-fit line for the data points.

(1)

(ii)Determine the height h0 of the water column at temperatureq = 0C.

.........................................................................................................................

.........................................................................................................................

(1)

(b)Explain why the results of this experiment suggest that the relationship between the height h and temperature q is of the form

h = h0(1 kq)

where k is constant.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

(4)

(c)Deduce that the value of k is approximately 4.8 103 deg C1.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

(3)

(d)The experiment is repeated using tubes with bores of different radii r but keeping the water temperature constant. The graph below shows the variation with

r

1

of the height h for capillary tubes of different radii r for a water temperature of 20C.

0.35

0.30

0.25

0.20

0.15

0.10

0.05

0

25.0

20.0

15.0

10.0

5.0

0

h

/ m

/ 10 m

1

r

3

1

It is suggested that capillary action is one of the means by which water moves from the roots of a tree to the leaves. A particular tree has a height of 25 m.

Use the graph to estimate the radius of the bore of the tubes that would enable water to be raised by capillary action from ground level to the top of the tree. Comment on your answer.

Estimate:.................................................................................................................

.................................................................................................................

.................................................................................................................

Comment:.................................................................................................................

.................................................................................................................

.................................................................................................................

(4)

(Total 13 marks)

88.This question is about measuring the permittivity of free space 0.

The diagram below shows two parallel conducting plates connected to a variable voltage supply. The plates are of equal areas and are a distance d apart.

V

d

variable voltage supply

+

The charge Q on one of the plates is measured for different values of the potential difference V applied between the plates. The values obtained are shown in the table below. The uncertainty in the value of V is not significant but the uncertainty in Q is 10%.

V / V

Q / nC 10%

10.0

30

20.0

80

30.0

100

40.0

160

50.0

180

(a)Plot the data points opposite on a graph of V (x-axis) against Q (y-axis).

(4)

(b)By calculating the relevant uncertainty in Q, add error bars to the data points (10.0, 30) and (50.0, 180).

(3)

(c)On the graph above, draw the line that best fits the data points and has the maximum permissible gradient. Determine the gradient of the line that you have drawn.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

(3)

(d)The gradient of the graph is a property of the two plates and is known as capacitance.Deduce the units of capacitance.

.....................................................................................................................................

(1)

The relationship between Q and V for this arrangement is given by the expression

Q =

V

d

A

0

where A is the area of one of the plates.

In this particular experiment A = 0.20 0.05 m2 and d = 0.50 0.01 mm.

(e)Use your answer to (c) to determine the maximum value of 0 that this experiment yields.

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

(4)

(Total 15 marks)

89.Data based question. This question is about change of electrical resistance with temperature.

The table below gives values of the resistance R of an electrical component for different values of its temperature T. (Uncertainties in measurement are not shown.)

T/C

1.2

2.0

3.5

5.2

6.8

8.1

9.6

R/

3590

3480

3250

3060

2880

2770

2650

(a)On the grid below, plot a graph to show the variation with temperature T of the resistance R. Show values on the temperature axis from T = 0C to T = 10C.

(3)

(b)(i)Draw a curve that best fits the points you have plotted. Extend your curve to cover the temperature range from 0C to 10C.

(1)

(ii)Use your graph to determine the resistance at 0C and at 10C.

Resistance at 0C = ...............................................

Resistance at 10C = .............................................

(2)

(c)On your graph, draw a straight-line between the resistance values at 0C and at 10C. This line shows the variation with temperature (between 0C and 10C) of the resistance, assuming a linear change.

(1)

(d)(i)Assuming a linear change of resistance with temperature, use your graph to determine the temperature at which the resistance is 3060 .

Temperature = .........................................................C

(1)

(ii)Use your answer in (d)(i) to calculate the percentage difference in the temperature for a resistance of 3060 that results from assuming a linear change rather than the non-linear change.

...........................................................................................................................

...........................................................................................................................

...........................................................................................................................

(3)

(Total 11 marks)