Physical Quantities, Units and Measurement：練習問題

Which of the following prefixes represents a factor of \(10^{-6}\)?

A student uses a micrometer screw gauge to measure the diameter of a thin wire. The instrument has a zero error of \(-0.02\text{ mm}\). When the student measures the wire, the main scale reads \(2.0\text{ mm}\) and the thimble scale reading is \(34\). Which of the following is the corrected diameter of the wire?

A rectangular metal plate has a mass of \(0.045\text{ kg}\). Its length is measured as \(5.00\text{ cm}\) and its width as \(20.0\text{ mm}\) using vernier calipers. If the thickness is measured as \(1.50\text{ mm}\) using a micrometer, what is the density of the metal in \(\text{kg/m}^3\)?

A student records the following measurements for different physical quantities. Which measurement is correctly expressed in its corresponding SI base unit?

The diameter of a planet is approximately \(1.3 \times 10^7\) m and the diameter of a large biological cell is approximately \(130\) \(\mu\)m. How many orders of magnitude larger is the planet compared to the cell?

Calculate the number of nanoseconds (ns) in a time interval of \(2.5\) milliseconds (ms), expressing your final answer in scientific notation.

The period of a simple pendulum is found by measuring the time taken for \(20\) complete oscillations using a stopwatch. If the total time recorded is \(34.2\) s, calculate the period and explain why measuring \(20\) oscillations is more precise than measuring just one.

A student uses a micrometer screw gauge to measure the diameter of a thin wire. The instrument shows a zero error of \(-0.03\) mm. If the main scale reading is \(2.50\) mm and the thimble scale reading is \(14\) divisions, calculate the actual diameter of the wire.

A student uses a pair of Vernier calipers to measure the diameter of a solid metal sphere.
(a) Explain why a micrometer screw gauge might be a better choice for measuring the diameter of a small wire compared to the Vernier calipers.
(b) The mass of the sphere is found to be \(156 \text{ g}\). If the measured diameter of the sphere is \(3.40 \text{ cm}\), calculate the density of the metal in \(\text{kg/m}^3\).
(c) State whether density is a scalar or a vector quantity.

A physicist is studying the properties of a new alloy.
(a) Distinguish between a base quantity and a derived quantity, using examples from the SI system.
(b) The physicist measures the current passing through a wire as \(500 \text{ mA}\). Calculate the total charge, in coulombs, that passes through a point in the circuit in \(2.0 \text{ minutes}\).
(c) If the volume of the alloy sample is \(2.5 \times 10^{-5} \text{ m}^3\), express this volume in \(\text{cm}^3\) and \(\text{mm}^3\).
(d) Compare the order of magnitude of the diameter of a typical atom to the diameter of the Earth.