Physical Quantities and Measurement Units
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Questions and Answers

What is the primary purpose of measurement in physics?

  • To perform calculations without accuracy
  • To quantitatively understand the natural world (correct)
  • To create experimental errors
  • To develop qualitative theories

    • Which of the following is a fundamental physical quantity?

  • Speed
  • Force
  • Area
  • Mass (correct)

    • What is a derived physical quantity?

  • Volume (correct)
  • Mass
  • Temperature
  • Time

    • Which unit is used for measuring length in the International System of Units (SI)?

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

    When discussing measurement systems, which of the following refers to temperatures being measured?

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

    What components are essential in defining a vector quantity?

    <p>Magnitude and direction</p> Signup and view all the answers

    What is an example of a physical quantity that can be measured?

    <p>Mass of a person</p> Signup and view all the answers

    Which of the following options represents SI prefixes?

    <p>Micro, Mega</p> Signup and view all the answers

    What is the value of $z$ in the dimensional equation derived?

    <p>$- rac{1}{2}$</p> Signup and view all the answers

    What is the dimensional formula for the gravitational constant $G$?

    <p>$M L^{-2} T^{-2}$</p> Signup and view all the answers

    Which of the following correctly balances the equation $x + z = 1$?

    <p>$x = rac{1}{2}$, $z = rac{1}{2}$</p> Signup and view all the answers

    What is the relationship between the dimensions of force, mass, and length in the formula $F = G rac{m_1 m_2}{r^2}$?

    <p>$F = M L^2 T^{-2}$</p> Signup and view all the answers

    Which aspect of dimensional analysis does $v = K rac{l^x m^y}{T^z}$ exemplify?

    <p>Homogeneity of dimensions</p> Signup and view all the answers

    What is the significance of negative dimensions in the dimensional equations discussed?

    <p>It shows an inverse relationship in dimensions.</p> Signup and view all the answers

    What is the unit of mass per unit length represented by $ u = rac{K}{ u_ ext{actual}}$?

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

    What does the CGS system stand for?

    <p>Centimeter-Gram-Second</p> Signup and view all the answers

    Which statement about dimensional analysis is true according to the provided information?

    <p>It leads to physical laws that require empirical validation.</p> Signup and view all the answers

    Which of the following systems is also known by the name French system of units?

    <p>MKS system</p> Signup and view all the answers

    What unit is defined as the mass of a platinum-iridium alloy cylinder?

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

    Which unit measures plane angle in the International System of Units?

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

    How is the meter defined in the International System of Units?

    <p>Length of a specific light path</p> Signup and view all the answers

    What is a unique characteristic of dimensions in physical quantities?

    <p>They represent qualitative nature.</p> Signup and view all the answers

    Which of these is a fundamental unit in the International System of Units?

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

    What denotes the dimension of length in physical quantities?

    <p>[L]</p> Signup and view all the answers

    What are fundamental dimensions?

    <p>Dimensions measured independently that express essential physical quantities.</p> Signup and view all the answers

    Which statement best describes derived dimensions?

    <p>They are products or quotients of fundamental dimensions.</p> Signup and view all the answers

    What is the primary purpose of dimension analysis?

    <p>To ensure each term in a physical equation has the same dimensions.</p> Signup and view all the answers

    What dimensions does the left-hand side (LHS) of the velocity equation $v = v_0 + at$ possess?

    <p>$[L][T^{-1}]$</p> Signup and view all the answers

    What is the result of dimensionally analyzing the formula $E = mc^2$?

    <p>Both sides of the equation have equivalent dimensions.</p> Signup and view all the answers

    Which of the following formulas represents a correct dimension analysis for wave speed?

    <p>$v = gh$</p> Signup and view all the answers

    In the context of dimension analysis, what does $[L][T^{-2}]$ represent?

    <p>Acceleration due to gravity.</p> Signup and view all the answers

    Why must the dimensions of the left-hand side (LHS) and the right-hand side (RHS) of an equation be the same?

    <p>To validate the physical significance of the equation.</p> Signup and view all the answers

    What is the correct representation of a force vector in the xy plane?

    <p>$F = A_x i + A_y j$</p> Signup and view all the answers

    Which of the following is a scalar quantity?

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

    What happens to the component Ax when the angle θ is 120°?

    <p>Ax is negative</p> Signup and view all the answers

    What is the unit vector in the positive z direction denoted as?

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

    Which equation correctly represents the resultant of vector A?

    <p>$A = \sqrt{A_x^2 + A_y^2}$</p> Signup and view all the answers

    What is the magnitude of a unit vector?

    <p>1</p> Signup and view all the answers

    How is a vector quantity differentiated from a scalar quantity?

    <p>Vectors have direction while scalars do not.</p> Signup and view all the answers

    What does the symbol 'mA' represent in electrical terms?

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

    Study Notes

    Physical Quantities

    • A physical quantity can be measured and described by a magnitude and unit.
    • Examples include: mass, length, area, temperature.

    Units of Measurement

    • A unit is the standard used to measure a physical quantity.
    • Common systems of units include:
      • CGS system: Centimetre-Gram-Second
      • MKS system: Metre-Kilogram-Second
      • FPS system: Foot-Pound-Second
      • International System of Units (SI): the preferred system globally

    International System of Units (SI)

    • SI uses seven fundamental units and two supplementary units.
    • Fundamental Units: Define the base quantities of the SI system.
      • Length: Metre (m) - defined as the distance travelled by light in a vacuum in 1/299,792,458 of a second.
      • Mass: Kilogram (kg) - defined by a platinum-iridium cylinder kept at the International Bureau of Weights and Measures.
      • Time: Second (s) - defined by the time taken for 9,192,631,770 oscillations of a cesium-133 atom.
      • Temperature: Kelvin (K) - the absolute temperature scale with 0 K being absolute zero.
      • Electric Current: Ampere (A) - defined as the constant current that, if maintained in two straight parallel conductors of infinite length and negligible circular cross-section placed one metre apart in vacuum, would produce between these conductors a force equal to 2 x 10^-7 Newton per metre of length.
      • Amount of Substance: Mole (mol) - the amount of substance that contains as many elementary entities as there are atoms in 0.012 kg of carbon-12.
      • Luminous Intensity: Candela (cd) - defined as the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 x 10^12 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.
    • Supplementary Units: Refer to plane angle and solid angle.
      • Plane Angle: Radian (rad) - an angle subtended at the center of a circle by an arc whose length is equal to the radius of the circle.
      • Solid Angle: Steradian (sr) - the solid angle subtended at the center of a sphere by its surface whose area is equal to the square of the radius of the sphere.

    Dimensions

    • The unique quality or type of every physical quantity that distinguishes it from all other quantities.
    • Refers to the qualitative nature of a physical quantity.
    • Examples:
      • Length: [L]
      • Mass: [M]
      • Time: [T]

    Fundamental and Derived Dimensions

    • Fundamental Dimensions: Measured independently and constitute the essential physical quantities (e.g., Length, Mass, Time).
    • Derived Dimensions: Expresses other quantities as products or quotients of fundamental dimensions (e.g., Area, Volume, Force)

    Dimensional Analysis

    • A method to check the correctness of a physical equation.
    • All terms in an equation must have the same dimensions; if they don't, the equation is incorrect.
    • Can also be used to derive physical laws.

    SI Prefixes

    • Used to express very large or very small quantities.
    • Examples:
      • milli (m): 10^-3
      • micro (µ): 10^-6
      • nano (n): 10^-9
      • pico (p): 10^-12
      • kilo (k): 10^3
      • mega (M): 10^6

    Vector and Scalar Quantities

    • Scalar Quantities: Measured with numbers and units only.
      • Examples: Length, Temperature, Time.
    • Vector Quantities: Measured with numbers and units, and have a specific direction.
      • Examples: Acceleration, Displacement, Force.

    Components of a Vector

    • Any vector can be represented by its horizontal and vertical components.
    • A vector A making an angle θ with the x-axis has:
      • Horizontal Component: Ax = A cosθ
      • Vertical Component: Ay = A sinθ

    Sign Convention for Vectors

    • The signs of a vector's components depend on the quadrant it's located in.
      • For example, if θ = 120°, Ax is negative and Ay is positive.

    Unit Vector Notation

    • A unit vector is a dimensionless vector with a magnitude of 1.
      • i: unit vector in the positive x direction.
      • j: unit vector in the positive y direction.
      • k: unit vector in the positive z direction.
    • A vector A can be expressed as:
      • A = Ax i + Ay j + Az k
      • Ax i is a vector of magnitude |Ax| lying on the x-axis.
      • Ay j is a vector of magnitude |Ay| lying on the y-axis.
      • Az k is a vector of magnitude |Az| lying on the z-axis.

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    Description

    This quiz covers the essential concepts of physical quantities, including their definitions, measurements, and the various systems of units used. Learn about the International System of Units (SI) and its fundamental components. Perfect for students seeking to solidify their understanding of measurement in physics.

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