## Dimensional Analysis – A solved example

Deduce the dimensional formula for workdone,pressure and density. [posted by boineelo ] Answer: workdone We know that workdone = force x distance Therefore [work done] =  [force] [distance] but force = ma [force]=[m][a] [a]=[velocity]/[t] [velocity]=[displacement]/[t] So, putting all these together [work done]=[m][distance][distance]/[time][time] [work done]=ML2T-2 Similarly, you can work out the dimensional formula for pressure and density as [pressure]=[force]/[area]=ML-1T-2 [...]