Question

If length 'L' force 'F' and time'T' are taken as fundamental quantities .What would be the dimensional equation of mass and density

Answer 1

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mass = Force / acceleration 

acc = L T⁻²
M =  F L⁻¹ T²

Density = Mass / Volume 
Density = F L⁻¹ T²  / L³
              = F L ⁻⁴ T² 
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Answer 2

Answer: mass= $F/LT^{-2}$ and density= $FL^{-4} T^{2}$

Explanation:

Since it is given that length L, force F, and time T are to be taken as fundamental quantities.

We have to find the dimensional equation for mass and density with these fundamental quantities.

We know that velocity= distance/time

Since distance can be taken as length as L

hence dimensional equation of velocity will be=L/T or $LT^{-1}$

Now we also know that acceleration = velocity/time

hence dimensional equation of acceleration= $LT^{-1}/T$ or $LT^{-2}$

Now we have Force= mass*acceleration

Since F has dimensional quantity as F hence dimensional equation for mass will be mass=force/acceleration

Mass= $F/LT^{-2}$ or $FL^{-1} T^{2}$ this will be the required dimensional equation for mass

Now we have another relation as Density= mass/volume

where volume is nothing but length*breadth*height

all length, breadth, and height are other forms of length hence they all have L as their fundamental quantity.

the hence dimensional equation for volume will be $L^{3}$

therefore, density has a dimensional equation as

density= $FL^{-1} T^{2}/L^{3}$ or $FL^{-4} T^{2}$ this will be the dimensional equation for density.

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