International System of Units Quiz

International System of Units

• The International System of Units (SI) was established in 1960 by an international committee.
• SI Units define standards for three basic quantities:
  • Mass : Kilogram (kg)
  • Length : Meter (m)
  • Time : Second (s)

Other Quantities

• Other quantities defined by the SI include:
  • Electric current : Ampere (Amp)
  • Temperature : Kelvin (K)
  • Luminous intensity : Candela
  • Amount of substances : mol

Other Systems of Units

• The CGS system uses centimeter (cm) for length, gram (gm) for mass, and second (s) for time.
• The MKS system uses meter (m) for length, kilogram (kg) for mass and second (s) for time.
• The British Engineering System uses Foot (ft) for length, Pound (lb) for mass, and second (s) for time.

Conversion of Units

• Units can be converted between systems.
• For example:
  • 1 mile = 1609 m = 1.609 km
  • 1 ft = 0.3048 m = 30.48 cm
  • 1 inch = 0.0254 m = 2.54 cm
  • 1 m = 100 cm
  • 1 kg = 1000 gm

Dimensional Analysis

• Dimension refers to the physical nature of a quantity.
• Basic dimensions in mechanics are:
  • Length (L)
  • Mass (M)
  • Time (T)

Dimensions of Physics Quantities

• Dimensions of some common physics quantities include:
  • Area: [A] = L.L = L²
  • Volume: [V] = L.L.L = L³
  • Velocity: [ν] = L / T = LT⁻¹
  • Acceleration: [a] = L / T² = LT⁻²
  • Momentum: [P] = [m].[ν] = MLT⁻¹
  • Kinetic Energy: [K.E] = [1/2].[m].[ν²] = M((LT⁻¹)²) = ML²T⁻²
  • Potential Energy: [P.E] = [m].[g].[h] = M(LT⁻²) L = ML²T⁻²

Dimensional Analysis Applications

• Dimensional analysis can be used to:
  • Check the validity of a formula
  • Derive some formulas

Example 2 : Deriving Formula for Distance Traveled

• Derive formula for distance (x) traveled by a car starting from rest with constant acceleration (a).
  • We assume distance is dependent on time (t) and acceleration (a): x α tⁿ aᵐ
  • Applying dimensional analysis:
    • = L
    • [tⁿaᵐ] = Tⁿ (LT⁻²)ᵐ = LᵐTⁿ⁻²ᵐ
  • Matching dimensions:
    • L = LᵐTⁿ⁻²ᵐ
  • Solving for m and n:
    • n-2m = 0
    • m = 1
    • n = 2
  • Therefore, x α t² a¹ or x = k at² (where k is a constant)

Example 3 : Analyzing a Power Law

• Determine power of radius (r) and velocity (v) to express centripetal acceleration (a) for an object moving in a circular orbit.
  • Assume a α rⁿ vᵐ.
  • Applying dimensional analysis:
    • [a] = LT⁻²
    • [rⁿvᵐ] = Lⁿ (LT⁻¹)ᵐ = Lⁿ⁺ᵐT⁻ᵐ
  • Solving for n and m:
    • n + m = 1
    • -m = -2
    • m = 2
    • n = -1
  • Therefore, a α r⁻¹v².

Test your knowledge of the International System of Units (SI) and its significance in defining mass, length, and time. This quiz also covers other unit systems like CGS and MKS, and the conversion between units. Challenge yourself and see how well you understand the basics of measurement!