Dimensional Analysis Quiz 1

Part A

See if you can determine the dimensions of the following quantities:

  1. volume

  2. acceleration (velocity/time)

  3. density (mass/volume)

  4. force (mass × acceleration)

  5. charge (current × time)

  1.  \(L^3\)
  2.  \(L/T^2\)
  3. \(M/L^3\)
  4. \(M\cdot L/T^2\)
  5. \(I\cdot T\)

Part B

Now find the dimensions of these:

  1. pressure (force/area)

  2. (volume)2

  3. electric field (force/charge)

  4. work (in 1-D, force × distance)

  5. energy (e.g., gravitational potential energy = mgh = mass × gravitational acceleration × height)

  6. square root of area

  1. \(M\cdot L^{-1}\cdot T^{-2}\)
  2. \(L^6\)
  3. \(M\cdot L\cdot I^{-1}\cdot T^{-3}\)
  4. \(M\cdot L^2/T^2\)
  5. \(M\cdot L^2/T^2\)
  6. \(L\)
NOTE: Dimensions of work = Dimensions of energy