Measurements

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

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.
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.

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 (1) 4. This question is about the photoelectric effect. Light is incident on a clean metal surface in a vacuum. The maximum kinetic energy KEmax of the electrons ejected from the surface is measured for different values of the frequency f of the incident light. The measurements are shown plotted below. (a) Draw a line of best fit for the plotted data points. (1) (b) Use the graph to determine (i) the Planck constant; ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (2) (ii) the minimum energy required to eject an electron from the surface of the metal (the work function). ........................................................................................................................... ........................................................................................................................... (3) (c) Explain briefly how Einstein’s photoelectric theory accounts for the fact that no electrons are emitted from the surface of this metal if the frequency of the incident light is less than a certain value. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (3) (Total 9 marks) 5. 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) 6. The ratio is approximately equal to A. 10–15. B. 10–8. C. 10–5. D. 10–2. (1) 7. 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) 8. 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) 9. 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) 10. This question is about an experiment designed to investigate Newton’s second law. In order to investigate Newton’s second law, David arranged for a heavy trolley to be accelerated by small weights, as shown below. The acceleration of the trolley was recorded electronically. David recorded the acceleration for different weights up to a maximum of 3.0 N. He plotted a graph of his results. (a) Describe the graph that would be expected if two quantities are proportional to one another. ..................................................................................................................................... ..................................................................................................................................... (2) (b) David’s data are shown below, with uncertainty limits included for the value of the weights. Draw the best-fit line for these data. (2) (c) Use the graph to (i) explain what is meant by a systematic error. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (2) (ii) estimate the value of the frictional force that is acting on the trolley. ........................................................................................................................... (1) (iii) estimate the mass of the trolley. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (2) (Total 9 marks) 11. 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) 12. 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. (1) 13. 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) 14. The time period T of oscillation of a mass m suspended from a vertical spring is given by the expression T = 2π where k is a constant. Which one of the following plots will give rise to a straight-line graph? A. T2 against m B. against C. T against m D. against m (1) 15. Which one of the following is a vector quantity? A. Electric power B. Electrical resistance C. Electric field strength D. Electric potential difference (1) 16. 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/Ω 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 = 0°C to T = 10°C. (3) (b) (i) Draw a curve that best fits the points you have plotted. Extend your curve to cover the temperature range from 0°C to 10°C. (1) (ii) Use your graph to determine the resistance at 0°C and at 10°C. Resistance at 0°C = ...............................................Ω Resistance at 10°C = .............................................Ω (2) (c) On your graph, draw a straight-line between the resistance values at 0°C and at 10°C. This line shows the variation with temperature (between 0°C and 10°C) 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 Ω. Temperature = .........................................................°C (1) (ii) Use your answer in (d)(i) to calculate the percentage difference in the temperature for a resistance of 3060 Ω that results from assuming a linear change rather than the non-linear change. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (3) (Total 11 marks) 17. 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) 18. 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) 19. 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) 20. 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) 21. Which one of the following is a scalar quantity? A. Pressure B. Impulse C. Magnetic field strength D. Weight (1) 22. Which one of the following is a fundamental unit? A. Coulomb B. Ohm C. Volt D. Ampere (1) 23. This question is about measuring the permittivity of free space ε0. 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. 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. Uncertainties in the data are not included. V / V Q / nC 10.0 30 20.0 80 30.0 100 40.0 160 50.0 180 (a) Plot a graph of V (x-axis) against Q (y-axis). (4) (b) Draw the line of best fit for the data points. (1) (c) Determine the gradient of your best-fit line. (2) ..................................................................................................................................... ..................................................................................................................................... (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 = where A is the area of one of the plates. In this particular experiment A = 0.20 m2 and d = 0.50 mm. (e) Use your answer to (c) to determine a value for ε0. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (3) (Total 11 marks) 24. 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 is A. 2%. B. 5%. C. 7%. D. 10%. (1) 25. Which one of the following is a fundamental unit? A. Coulomb B. Ohm C. Volt D. Ampere (1) 26. This question is about measuring the permittivity of free space ε0. 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. 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 = 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 ε0 that this experiment yields. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (4) (Total 15 marks) 27. 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) 28. 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) 29. Which of the following is the best estimate, to one significant digit, of the quantity shown below? A. 1.5 B. 2.0 C. 5.8 D. 6.0 (1) 30. Two objects X and Y are moving away from the point P. The diagram below shows the velocity vectors of the two objects. Which of the following velocity vectors best represents the velocity of object X relative to object Y? (1)

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