Question

Dimensional Analysis: Call m_Planck the unit of mass in a system of units in which G, c and h, all have the value 1 times the combination of units with the appropriate dimensions. What is the volume in SI units of a mass of water equal to m_Planck? What is the volume in SI units of m_Planck of air? (Answer should be in SI unit)

Answer 1

Plancks units of Mass are defined in fundamental constants in Planck units as

  ( where )

Then in SI units, m_p has the value as

  

a). Now when mass of water= mPlanck= m_p

or   

Density of water is

Then we know that Volume= Mass/ Density

Using all known values, Volume of water is (ANS)

b).Now when mass of air= mPlanck= m_p

or   

Density of air is

Then we know that Volume= Mass/ Density

Using all known values, Volume of air is (ANS)