Units and Measurements

Physics is a quantitative science, and every physical quantity must be measured by comparing it with an accepted standard called a unit. A measurement is a number with a unit. This chapter explains fundamental or base quantities, whose units are chosen independently, and derived quantities, whose units are combinations of the base units. You will study the International System of Units (SI), with its seven base units: the metre, kilogram, second, ampere, kelvin, mole and candela. The radian and steradian are used for plane and solid angles, and prefixes such as kilo, milli and micro express very large and very small values. The chapter explains significant figures, the rules for counting them, rules for rounding off, and how to report the results of addition, subtraction, multiplication and division. You will then learn the dimensions of physical quantities and write dimensional formulae such as [M L T^-2] for force. Dimensional analysis is used to check the consistency of equations, to deduce relations among physical quantities and to convert units. Its limitations are also discussed.

Detailed Worksheet: Units and Measurements Section A - Definitions (10 marks) 1. Name the seven SI base quantities and their units. (2 marks) 2. State the number of significant figures in (i) 0.007 m^2 (ii) 2.64 x 10^24 kg (iii) 0.2370 g/cm^3 (iv) 6.320 J. (2 marks) 3. Write the dimensional formula of force and of pressure. (2 marks) 4. State the principle of homogeneity of dimensions. (2 marks) 5. Name two dimensionless quantities. (2 marks) Section B - Calculations and Applications (15 marks) 6. Round off 2.745 and 2.735 to three significant figures, and state the rule used. (3 marks) 7. Add 436.32 g, 227.2 g and 0.301 g, and give the answer to the correct number of significant figures. (3 marks) 8. Check the dimensional correctness of the equation v^2 = u^2 + 2as. (3 marks) 9. Find the dimensional formula of the gravitational constant G from F = Gm1m2/r^2. (3 marks) 10. Convert 1 joule into ergs using dimensional analysis. (3 marks) Section C - Diagrams (10 marks) 11. Draw a table showing the seven SI base quantities, their units and symbols. (4 marks) 12. Draw a diagram to explain plane angle in radians and solid angle in steradians. (3 marks) 13. Draw a flow chart showing the steps to deduce a formula using dimensional analysis. (3 marks) Section D - Analysis and Higher-order Thinking (15 marks) 14. Using dimensional analysis, show that the period of a simple pendulum is T = k sqrt(l/g), assuming it depends on the length l, the mass m of the bob and g. (5 marks) 15. The centripetal force on a body moving in a circle depends on its mass m, speed v and the radius r. Use dimensional analysis to find the formula. (5 marks) 16. State the uses and the limitations of dimensional analysis with examples. (5 marks) Instructions: Time allowed 2 hours. Attempt all sections. Give answers to the correct number of significant figures. Use M, L and T for the dimensions of mass, length and time.