Measurements 85 Multiple Choice Questions

32 

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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 W

B. 2.4 W

C. 2.40 W

D. 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 s–1. The current flows at 0.6 m s–1 in the direction shown.

0 . 8 m s

B o a t

B a n k

B a n k – 1

– 1 0 . 6 m s

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. eV

B. W s–1

C. W m–1

D. N m s–1

(2)

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. 10–15.

B. 10–8.

C. 10–5.

D. 10–2.

(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

(3)

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 Ω. Which one of the following gives the resistance to an appropriate number of significant figures?

A. 5.3 Ω

B. 5.32 Ω

C. 5.318 Ω

D. 5.31765775 Ω

(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 N

B. 3 N

C. 5 N

D. 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. 10–8 m.

B. 10–15 m.

C. 10–23 m.

D. 10–30 m.

(4)

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

A. 1.6 × 1019 J.

B. 1.0 J.

C. 1.6 × 10–19 J.

D. 9.1 × 10–31 J.

(1)

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

expression

T = 2π k m

where k is a constant.

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

A. T2 against m

B. T against m

C. T against m

D. T against m

(1)

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

A. Electric power

B. Electrical resistance

C. Electric field strength

D. Electric potential difference

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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. 10–12 m.

B. 10–15 m.

C. 10–18 m.

D. 10–21 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.

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

A. Pressure

B. Impulse

C. Magnetic field strength

D. Weight

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

A. Coulomb

B. Ohm

C. Volt

D. Ampere

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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. Coulomb

B. Ohm

C. Volt

D. Ampere

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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. N

B. N s–1

C. N m2 s–1

D. N m–2 s

(1)

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

below?

15.9

1 . 8  π

A. 1.5

B. 2.0

C. 5.8

D. 6.0

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7 t25.Two objects X and Y are moving away from the point P. The diagram below shows the velocity vectors of the two objects.

P V e l o c i t y v e c t o r f o r o b j e c t Y

V e l o c i t y v e c t o r f o r o b j e c t X

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

A . B .

C . D .

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26. A student measures two lengths as follows: T = 10.0  0.1 cm

S = 20.0  0.1 cm.

The student calculates:

FT, the fractional uncertainty in T

FS, the fractional uncertainty in S

FT–S, the fractional uncertainty in (T – S)

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

Which of these uncertainties has the largest magnitude?

A. FT

B. FS

C. FT–S

D. FT+S

(1)

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

p o i n t P

y –d i r e c t i o n

p o i n t Q

x– d i r e c t i o n

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

(10)

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

A .

C .

B .

D . P

P

P

P Q

Q

Q

Q

dX

dX

d X

dX d Y

d Y

d Y

d Y dR

d R

d R

d R

(1)

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

A. 10–4 N.

B. 10–2 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

(11)

30. The reading of a constant potential difference is made four times by a student. The readings are 1.176 V

1.178 V 1.177 V 1.176 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

g r a d i e n t = a

B .

v

0

u

0 t

g r a d i e n t = 1

a

C .

v

0 0 u t

g r a d i e n t = a

D .

v

0 0 u t

g r a d i e n t = 1

a

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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 π 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 = πr2h.

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%.

(13)

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 1 0

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

A. (6.0 ± 0.5)°C

B. (6.1 ± 0.1)°C

C. (6.2 ± 0.2)°C

D. (6.2 ± 0.5)°C

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37. Which of the following represents two vector quantities?

A. distance, acceleration

B. kinetic energy, work

C. force, momentum

D. 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. 10–23 kg.

B. 10–25 kg.

C. 10–27 kg.

D. 10–29 kg.

(1)

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

A. Ampere

B. Volt

C. Ohm

D. Tesla

(15)

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

A. 0.006 m

B. 0.06 m

C. 600 m

D. 620 m

(1)

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

l

g

f

2

1

where g and  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. 10–23 kg.

B. 10–25 kg.

C. 10–27 kg.

(16)

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 s−2. 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 s−1

B. 14.0 m s−1

C. 14.00 m s−1

D. 14.000 m s−1

(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

22

.

T

r

Which of the following graphs would produce a straight-line? A. a against T

B. a against T2

C. a against

T

1

(17)

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 relation c = 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.

(18)

49. The mass of an electron is 9.1  10–31 kg and that of a proton is 1.7  10–27 kg. Which one of the following is the difference in the order of magnitude of the masses of the electron and the proton?

A. 10.8

B. 7.4

C. 5.4

D. 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-

(19)

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

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

1 0 9 8 7 6 5 4 3 2 c m

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

A. 5  0.1 cm

B. 5  0.2 cm

C. 5.0  0.1 cm

D. 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

1 nP

1 nP

0

Which one of the following is the correct expression for the variation of P with x? A. P = P0 e−gx

B. P = P0 e+gx

C. P = P0 + e−gx D. P = P0 − e+gx

(21)

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. Work

B. Temperature

C. Electric field

D. 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.

(22)

58. The period T of oscillation of a mass m attached to the end of a spring is given by 2 ,

k m

T 

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. 10–2 s.

B. 10–1 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.

(23)

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 P2

B. v2 against P

C. v against P D. 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. 10–7 s

B. 10–8 s

C. 10–9 s

D. 10–10 s

(24)

64. The grid below shows one data point and its associated error bar on a graph. The x-axis is not shown.

5 . 0

4 . 0

3 . 0

2 . 0

1 . 0

Which of the following is the correct statement of the y-value of the data point, with its uncertainty?

A. 3  0.2

B. 3.0  0.2

C. 3.0  0.20

D. 3.00  0.20

(1)

65. A resistor of resistance R is connected across the terminals of a battery of emf E and internal

resistance r. The current I in the circuit is measured using an ammeter. r

E

I

R

A

Which of the following assumptions is made in order that E, R, r and I are related by the equation below?

E = I(R + r)

A. The resistor of resistance R obeys Ohm’s law.

B. The resistance R is much greater than the internal resistance r.

(25)

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)

67. 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.

1 gy

I

0 0

1 gx

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

A. – I

B. + I

C. – lg I

D. + lg I

(26)

A. ampere newton second

B. volt second kelvin

C. mole ampere kilogram

D. kilogram metre tesla

(1)

69. The mass of a body is measured to be 0.600 kg and its acceleration to be 3 m s–2. 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)

70. 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)

71. 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

(27)

(1)

72. 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

(1)

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

least → greatest

A. α-particle β-particle proton

B. proton α-particle β-particle

C. proton β-particle α-particle

D. β-particle proton α-particle

(1)

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

A. 6.0×104 J .

B. 6.0×104W .

C. 3.6×106 J .

D. 3.6×106W .

(1)

75. Which of the following contains three scalar quantities?

A. mass charge speed

B. density weight mass

C. speed weight charge

(28)
(29)

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

s e t - s q u a r e

m e t r e r u l e h e i g h t t o

b e m e a s u r e d

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 of set-square

error caused by non-vertical ruler

A. random random

B. random systematic

C. systematic random

D. systematic systematic

(30)

77. 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. –lnR0

B.

k R0 ln 

C. lnR0

D.

k R0 ln

(1)

78. An elephant has a life expectancy of 60 years. Which of the following gives the order of

magnitude of this lifetime?

A. 1011s

B. 109s

C. 107s

D. 105s

(31)

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

f =



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 1

B. f 2 

C. f

D. f

1

(1)

80. 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

(32)

81. Which of the following graphs shows the best-fit line for the plotted points?

A . y

0

B . y

0

0 x 0 x

C . y

0

D . y

0

0 x 0 x

(1)

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

k m π

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)

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

A. 10–4 N.

B. 10–2 N.

C. 1 N.

(33)

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

V M

ρ 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)

85. 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.

Figure

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