Show dimensions are equivalent

A question is this type if and only if it asks to prove that two different physical quantities (like energy density and pressure) have the same dimensions.

1 questions · Moderate -0.5

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OCR MEI Further Mechanics Minor 2024 June Q2
8 marks Moderate -0.5
2
  1. State the dimensions of force. Use the following metric-imperial conversion factors for the rest of this question.
    A unit of force used in the imperial system is the pound-force (lbf). 1 lbf is defined as the gravitational force exerted on 1 lb on the surface of the Earth.
  2. Show that 1 lbf is approximately equal to 4.45 N . The pascal (Pa) is a unit of pressure equivalent to 1 Newton per square metre. Pressure can also be measured in pound-force per square inch (psi). A diver, at a depth of 40 m , experiences a typical pressure of \(5 \times 10 ^ { 5 } \mathrm {~Pa}\).
  3. Determine whether this is greater or less than the pressure in a bicycle tyre of 80 psi . In various physical contexts, energy density is the amount of energy stored in a given region of space per unit volume.
  4. Show that energy density and pressure are dimensionally equivalent.