Physics Chapter 1.1 on Units and Dimensions
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Questions and Answers

What is the multiplicative value represented by the prefix 'giga'?

  • 10^3
  • 10^12
  • 10^9 (correct)
  • 10^6

    • Which prefix corresponds to the multiplicative value of 0.001?

  • deci
  • milli (correct)
  • centi
  • micro

    • If a unit is expressed as 10^12, which prefix is used?

  • mega
  • tera (correct)
  • kilo
  • giga

    • What is the wavelength of light emitted by a laser at 600nm in meters?

    <p>6.0 x 10^-7 m</p> Signup and view all the answers

    Which of these prefixes indicates a factor of 10^-6?

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

    What is the multiplicative value represented by the prefix 'kilo'?

    <p>10^3</p> Signup and view all the answers

    Which of the following correctly identifies the prefix for 0.01?

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

    What is the scientific notation for the prefix 'pico'?

    <p>10^-12</p> Signup and view all the answers

    Which of the following is a scalar quantity?

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

    What is the unit for measuring electric current in the International System of Units (SI)?

    <p>Ampere (A)</p> Signup and view all the answers

    Which of the following quantities is expressed in derived SI units?

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

    A physical quantity that has both magnitude and direction is known as a:

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

    In the SI system, which of the following is the base unit for measuring time?

    <p>Second (s)</p> Signup and view all the answers

    What prefix would be used to denote one billionth of a unit in the SI system?

    <p>Nano-</p> Signup and view all the answers

    Which of the following is NOT one of the base SI units?

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

    What is the dimension of pressure in the SI system?

    <p>Force per unit area</p> Signup and view all the answers

    What does dimensional analysis help to determine?

    <p>The dimensions of a variable using other variables</p> Signup and view all the answers

    How does Newton's law of universal gravitation express the relationship between force, mass, and distance?

    <p>F is directly proportional to the masses and inversely proportional to the distance squared</p> Signup and view all the answers

    Which of the following is a scalar quantity?

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

    What characterizes vector quantities?

    <p>They are defined by both magnitude and direction</p> Signup and view all the answers

    What are the dimensions of force?

    <p>Mass times length divided by time squared</p> Signup and view all the answers

    What does G represent in the equation for universal gravitation?

    <p>The gravitational constant</p> Signup and view all the answers

    What can a vector field describe?

    <p>Magnitude and direction at each point in space</p> Signup and view all the answers

    Which of the following statements about the dimensions of G is correct?

    <p>The dimensions of G are equal to force times distance squared divided by mass squared</p> Signup and view all the answers

    How is the magnitude of the x-component of a vector represented mathematically?

    <p>$Ax = lAl cos heta$</p> Signup and view all the answers

    What does the length of an arrow in vector representation indicate?

    <p>The magnitude of the vector</p> Signup and view all the answers

    What is the relationship between the angle θ and the vector components Ax and Ay?

    <p>$ heta$ determines the ratio of Ax to Ay.</p> Signup and view all the answers

    In a right triangle formed by vector components, what does the hypotenuse represent?

    <p>The vector's magnitude</p> Signup and view all the answers

    Which trigonometric ratio is used to derive the y-component (Ay) of a vector?

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

    What does the notation A = (Ax, Ay) signify?

    <p>A represents a vector with its x and y components.</p> Signup and view all the answers

    Which statement accurately describes the direction of a vector?

    <p>It is indicated by the angle θ relative to the x-axis.</p> Signup and view all the answers

    How do the components of a vector traditionally align in a two-dimensional coordinate system?

    <p>They are always perpendicular to each other.</p> Signup and view all the answers

    What method can be used to add two vectors graphically?

    <p>The tip-to-tail method</p> Signup and view all the answers

    How are the x and y components of two vectors A and B combined?

    <p>A + B = (Ax + Bx, Ay + By)</p> Signup and view all the answers

    What theorem is used to determine the magnitude of a vector from its components?

    <p>Pythagorean theorem</p> Signup and view all the answers

    What is the resulting vector when vector A = (0 m, 1 m) and vector E = (0 m, 20 m) are subtracted?

    <p>(0 m, 19 m)</p> Signup and view all the answers

    What does the resultant vector represent in vector addition?

    <p>The vector connecting the tail of the first vector to the tip of the second vector</p> Signup and view all the answers

    Which of the following best describes the relationship between the components and the magnitude of a vector?

    <p>The magnitude is the square root of the sum of the squares of the components.</p> Signup and view all the answers

    What is the correct expression for the sum of two vectors A and B in terms of their individual components?

    <p>A + B = (Ax + Bx, Ay + By)</p> Signup and view all the answers

    If vector A has a magnitude of $|A|$ and an angle of $ heta$ with the x-axis, what are the x and y components of vector A?

    <p>($|A| ext{cos}( heta), |A| ext{sin}( heta)$)</p> Signup and view all the answers

    Study Notes

    Units and Dimensions

    • Physical quantities have dimensions (mass, temperature, length, time) and units.
    • SI (International System of Units) is a common system of units.
    • SI base units include meter (m), kilogram (kg), second (s), Kelvin (K), ampere (A), mole (mol).
    • Derived SI units are combinations of base SI units (e.g., force, energy, pressure).
    • Prefixes can be added to SI units to represent large or small values (e.g., kilometer (km), nanometer (nm)).

    Dimensional Analysis

    • Dimensions are the units of a variable and are expressed in square brackets (e.g., [X]).
    • In an equation, the dimensions of the left side must equal the dimensions of the right side.
    • Dimensional analysis can be used to determine the dimensions of unknown variables in an equation.

    Scalars and Vectors

    • Scalars have only magnitude (e.g., mass, time, temperature).
    • Vectors have both magnitude and direction (e.g., displacement, velocity, acceleration, force, momentum).
    • Vectors can be represented graphically as arrows: the length represents magnitude, and the direction of the arrow indicates the direction.
    • Vectors can be represented component-wise: A = (Ax, Ay), where Ax and Ay are the x- and y-components of the vector, respectively.
    • The magnitude of a vector A can be found using the Pythagorean theorem: |A| = √(Ax² + Ay²).

    Vector Addition

    • Vectors can be added graphically using the tip-to-tail method.
    • Vectors can be added component-wise: A + B = (Ax + Bx, Ay + By).
    • The difference of two vectors can be determined using vector subtraction, where the negative of one vector is added to the other.
    • Vector subtraction is equivalent to adding the opposite vector.

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    Description

    Explore the fundamental concepts of units and dimensions in physics. This quiz covers the International System of Units (SI), dimensional analysis, and the distinction between scalars and vectors. Test your understanding through various questions related to these essential topics.

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