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Dimensional Analysis – A solved example

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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

[density]=[mass]/[volume]=ML-3

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