SI Units for Plane Angle and Solid Angle
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Questions and Answers

What is a unit in the context of measuring physical quantities?

  • A common language for scientists
  • A standard to compare with (correct)
  • A random number assigned to a quantity
  • A formula to calculate dimensions

    • Why do we need only a limited number of units to express all physical quantities?

  • Because units are derived from base units (correct)
  • Because units are arbitrary
  • Because units are specific to each country
  • Because physical quantities are not interrelated

    • What are the units for fundamental or base quantities called?

  • Fundamental units (correct)
  • Primary units
  • Random units
  • Derived units

    • What do we call the units obtained for physical quantities that are derived from base units?

    <p>Derived units</p> Signup and view all the answers

    What is a complete set of base and derived units known as?

    <p>System of units</p> Signup and view all the answers

    Why did scientists from different countries use different systems of units in the past?

    <p>Lack of a universally accepted system</p> Signup and view all the answers

    What is the unit for plane angle?

    <p>Radian</p> Signup and view all the answers

    Which SI unit represents mass?

    <p>Kilogram</p> Signup and view all the answers

    How is the second defined in the SI system?

    <p>In terms of the caesium frequency</p> Signup and view all the answers

    What is the symbol for the SI unit of electric current?

    <p>A</p> Signup and view all the answers

    Which quantity has a dimensionless unit?

    <p>Plane angle</p> Signup and view all the answers

    What represents the SI unit of length?

    <p>$m$</p> Signup and view all the answers

    How many significant figures does the number 0.004700 km have?

    <p>4</p> Signup and view all the answers

    What is the best way to remove ambiguities in determining the number of significant figures?

    <p>Reporting every measurement in scientific notation</p> Signup and view all the answers

    In scientific notation, how is a number typically expressed?

    <p>a × 10^b (where a is between 1 and 10, and b is any positive or negative exponent of 10)</p> Signup and view all the answers

    What happens to the number of significant figures when changing units in a measurement?

    <p>The significant figures remain the same</p> Signup and view all the answers

    When rounding off a number in scientific notation, what value should 'a' be rounded to if 'a' is less than or equal to 5?

    <p>'a' should be rounded to 5</p> Signup and view all the answers

    What are the base units for length, mass, and time in the MKS system?

    <p>Metre, kilogram, second</p> Signup and view all the answers

    Which organization developed the standard scheme of symbols, units, and abbreviations for the SI system in 1971?

    <p>Bureau International des Poids et Measures</p> Signup and view all the answers

    Why are conversions within the SI system considered simple and convenient?

    <p>Due to the use of the decimal system in SI units</p> Signup and view all the answers

    In SI, how many base units are there according to Table 1.1?

    <p>Seven</p> Signup and view all the answers

    What is the unit defined for plane angle dθ in SI?

    <p>Radians</p> Signup and view all the answers

    How is solid angle dΩ defined in SI?

    <p>Ratio of intercepted area to square of radius</p> Signup and view all the answers

    What is the rule provided for determining the significant figures when all zeros are between two non-zero digits?

    <p>All zeros are significant, regardless of the location of the decimal point.</p> Signup and view all the answers

    If a number is less than 1, which zeros are not considered significant?

    <p>Zeros on the left of the first non-zero digit</p> Signup and view all the answers

    In the number 0.06900, how many significant figures are there?

    <p>Four</p> Signup and view all the answers

    What is the significance of the trailing zeros in a number with a decimal point?

    <p>They are always considered significant.</p> Signup and view all the answers

    Why are the zeros in 4.700 m considered significant?

    <p>To indicate precision of measurement</p> Signup and view all the answers

    How many significant figures does 123000 mm have?

    <p>Four</p> Signup and view all the answers

    Study Notes

    Units and Measurement

    • A unit is a standard quantity used to express physical quantities.
    • Only a limited number of units are needed to express all physical quantities because they can be combined to express derived quantities.
    • The units for fundamental or base quantities are called base units.
    • The units obtained for physical quantities that are derived from base units are called derived units.
    • A complete set of base and derived units is known as a system of units.

    SI System

    • The SI system is a widely used system of units that consists of 7 base units.
    • The SI unit for plane angle is the radian (rad).
    • The SI unit for mass is the kilogram (kg).
    • The second is defined in the SI system as the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom.
    • The symbol for the SI unit of electric current is the ampere (A).
    • The quantity that has a dimensionless unit is the plane angle.

    Significant Figures

    • The number 0.004700 km has 4 significant figures.
    • The best way to remove ambiguities in determining the number of significant figures is to use scientific notation.
    • In scientific notation, a number is typically expressed as a × 10^n, where a is between 1 and 10.
    • The number of significant figures does not change when changing units in a measurement.
    • When rounding off a number in scientific notation, if 'a' is less than or equal to 5, it should be rounded to 0.
    • If a number is less than 1, the leading zeros are not considered significant.
    • The rule for determining the significant figures when all zeros are between two non-zero digits is that the zeros are considered significant.
    • The significance of the trailing zeros in a number with a decimal point is that they are considered significant.
    • The zeros in 4.700 m are considered significant because they are trailing zeros with a decimal point.
    • The number 123000 mm has 4 significant figures.

    Other Systems

    • The MKS system is another system of units that uses meter, kilogram, and second as base units.
    • The organization that developed the standard scheme of symbols, units, and abbreviations for the SI system in 1971 is the International Committee for Weights and Measures.
    • Conversions within the SI system are considered simple and convenient because the units are based on the decimal system.

    Angles

    • The unit defined for plane angle dθ in SI is the radian (rad).
    • The solid angle dΩ is defined in SI as the ratio of the area of the sphere subtended by the angle to the square of the radius of the sphere.

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    Description

    Learn about the SI units for plane angle (radian) and solid angle (steradian) which are both dimensionless quantities. Explore the definitions and symbols of radian (rad) and steradian (sr), along with other SI base quantities and units.

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