Physical Quantities and Units Quiz
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Questions and Answers

What are the dimensions of kinetic energy?

  • M L^2 T^-1
  • M L^2 T^-2 (correct)
  • M L T^-2
  • M L T^-1

    • In the equation $d \sin \theta = n \lambda$, which part is dimensionless?

  • $\sin \theta$
  • d
  • $\lambda$
  • n (correct)

    • What is the correct dimensional formula for potential energy?

  • M T^2
  • M L^2 T^-1
  • M L^2 T^-2 (correct)
  • M L T^-2

    • What is the dimension of acceleration in Newton's second law?

    <p>L T^-2</p> Signup and view all the answers

    What is the dimension of the spring constant K in Hooke's law?

    <p>M L^-1 T^-2</p> Signup and view all the answers

    Which of the following formulas represents velocity?

    <p>$v = \frac{Distance}{Time}$</p> Signup and view all the answers

    What are the dimensions of pressure according to the provided formulas?

    <p>$M L^{-1} T^{-2}$</p> Signup and view all the answers

    Which of the following conversions is correct?

    <p>1 inch = 0.0254 m</p> Signup and view all the answers

    What is the derived dimension of density?

    <p>$M L^{-3}$</p> Signup and view all the answers

    Which statement accurately describes derived quantities?

    <p>Derived quantities are formed by combining fundamental quantities.</p> Signup and view all the answers

    What is the formula used to calculate acceleration?

    <p>$a = \frac{Change \ in \ Velocity}{Time}$</p> Signup and view all the answers

    Which of the following correctly states the relationship between mass and momentum?

    <p>Momentum is directly proportional to mass and velocity.</p> Signup and view all the answers

    What is the correct unit for pressure in terms of the SI system?

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

    What is the dimension of the force in terms of mass, length, and time?

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

    Which of the following represents the dimension of the spring constant K?

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

    In the expression x ⍺ a^n * t^m, what do the variables n and m represent?

    <p>The exponents that indicate the degree of proportionality</p> Signup and view all the answers

    What condition must hold for the exponents of L and T on both sides of the equation x ⍺ a^n * t^m?

    <p>They must be the same</p> Signup and view all the answers

    From the derivation provided, what is the value of n in the equation x ⍺ a^n * t^m?

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

    What is the derived equation for m based on the equalities of dimensional analysis?

    <p>m = 2</p> Signup and view all the answers

    What is the formula that relates the force of attraction between two masses m1 and m2?

    <p>F = G * m1 * m2 / r^{2}</p> Signup and view all the answers

    What is the dimensional formula for the gravitational constant G?

    <p>M^{-1} * L^{2} * T^{-2}</p> Signup and view all the answers

    What is the dimensional formula for the periodic time T of a simple pendulum?

    <p>M^0 L^0 T^1</p> Signup and view all the answers

    Which value of α satisfies the dimensional analysis for the equation T = k L^α g^γ?

    <p>1/2</p> Signup and view all the answers

    What is the acceleration due to gravity represented as in the dimensional analysis?

    <p>L T^-2</p> Signup and view all the answers

    Given that speed was calculated as 38 m/s, what was the result when converted to mi/h?

    <p>84.96 mi/h</p> Signup and view all the answers

    If the relationship for force in terms of mass and velocity is v^2 = 2C1 sin(2pC2t), what does v represent?

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

    What does the variable C1 represent in the context of dimensional analysis?

    <p>Constant derived from geometry</p> Signup and view all the answers

    In the equation for work, W = 2t^2C1 - 3m x C2, which terms are primarily associated with energy dimensions?

    <p>2t^2C1</p> Signup and view all the answers

    What is the value of β in the law T = k L^α m^β g^γ based on dimensional analysis?

    <p>0</p> Signup and view all the answers

    Study Notes

    Physical Quantities

    • Fundamental quantities are independent and cannot be derived from other quantities:
      • Mass (M)
      • Length (L)
      • Time (T)
    • Derived quantities can be expressed in terms of fundamental quantities:
      • Speed = distance travelled / time = length / time
    • Other derived quantities:
      • Density = Mass / Volume = M / (L^3)
      • Velocity = distance / time = L / T
      • Acceleration = Velocity / time = (L/T) / T = L/T^2
      • Pressure = Force / Area = (M * L * T^-2) / (L ^ 2) = M * L^-1 * T^-2

    Systems of Units

    • Meter (m), kilogram (kg), second (s) are the base units of the International System of Units (SI)
    • Different systems of units exist, including the centimetre-gram-second (CGS) system and the US customary units

    Conversion Factors

    • 1 meter (m) = 100 centimeters (cm) = 39.4 inches (in) = 3.28 feet (ft) = 6.21 × 10-4 miles (mi)
    • 1 inch (in) = 2.54 centimeters (cm) = 0.0254 meters (m)
    • 1 foot (ft) = 0.305 meters (m) = 30.5 centimeters (cm)
    • 1 mile (mi) = 1610 meters (m) = 1.61 kilometers (km)

    Dimensional Analysis

    • Dimensional analysis helps to verify the correctness of physical equations by checking if the dimensions on both sides of the equation are consistent.
    • The dimensions of a quantity are expressed in terms of the fundamental quantities, like M, L, and T.

    Examples

    • Example 1: Kinetic energy (E) and potential energy (E) can be added because they have the same dimension: M * L^2 * T^-2
    • Example 2: Young's double-slit experiment equation: d * sin(θ) = n * λ, confirms that both sides have the dimension of Length (L).
    • Example 3: Dimension of spring constant (K) can be deduced using Hooke's law (F = -Kx) and Newton's second law (F = ma): K = M * T^-2.
    • Example 4: Using dimensional analysis to derive the expression of x (length) in terms of acceleration (a) and time (t): x = a * t^2.
    • Example 5: The dimension of the gravitational constant (G) is determined by the equation for gravitational force (F = G * m1 * m2 / r^2): G = M^-1 * L^3 * T^-2
    • Example 6: Dimensional analysis is used to find the relationship between the period (T) of a simple pendulum and its length (L), mass (m), and acceleration due to gravity (g): T = k * sqrt(L/g).
    • Example 7: Converting speed from meters per second (m/s) to miles per hour (mi/h): 38 m/s = 84.96 mi/h.
    • Example 8: Using dimensional analysis to determine the constants C1 and C2 in relationships involving distance, time, force, work, mass, velocity, and energy.

    Key Takeaways

    • Dimensional analysis is a valuable tool for checking the consistency of physical equations and deriving relationships.
    • It’s important to understand the fundamental and derived quantities, their dimensions, and their units.
    • Conversion factors are essential to ensure that calculations are carried out using consistent units.

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    Description

    Test your understanding of physical quantities, including fundamental and derived quantities, as well as the various systems of measurement. Explore the International System of Units (SI) and conversion factors between different units. This quiz will help solidify your knowledge in physics.

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